(CBS) In 1991, 16 years after Martha’s murder, the case was revived when a new investigator started taking another look at the Skakels.

With the focus back on his family, Rushton Skakel did something extraordinary: He tried to clear the family name.

He hired his own team of investigators to look into Martha's death, and their results became known as the Sutton Report. The key findings focused on Littleton as well as Tommy and Michael Skakel. But the effort backfired after the report, for the first time ever, pointed a finger at Michael.

“Michael lied to the police,” says Levitt. “Michael's story was he's gone to the Terrians, he comes home at 11.30 p.m. and then he goes right to bed.”

But, he told Sutton investigators that it was not all he did that night. Around midnight, Michael said he was drunk and wanted to see Martha. He went out, climbed a tree outside Martha’s window, threw stones at the window and then masturbated in a tree. While climbing down, he said he heard voices right around where the crime scene took place, and ran home.

Michael even made a tape recording of that story in a 1997 book proposal for a tell-all biography: “I remember thinking, 'Oh, my God! If I tell anyone I was out that night, they’re going to think I did it.'"

*****

When former L.A. detective Mark Fuhrman was leaked a copy of the Sutton report, he wrote the best seller, "Murder in Greenwich," naming Michael as Martha’s killer.

“Michael Skakel puts himself at the crime scene, and Michael Skakel makes admissions that only a murderer would make,” says Fuhrman.

Just one month later, in June 1998, prosecutor Jonathon Benedict called for a special grand jury to hear evidence about the case. The grand jury heard some explosive testimony, much of it from Michael's former classmates at the Elan Reform School. Several of them also dropped a bombshell -- that Michael had confessed to killing Martha.

"The first words he ever said to me was, 'I'm going to get away with murder. I'm a Kennedy,'" says former Elan student Greg Coleman. “He made advances to her, and she rejected his advance. He drove her skull in with a golf club."

In January 2000, after hearing testimony from several Elan students and others, the grand jury indicted Michael for the murder of Martha Moxley.

When Michael finally went to trial, the rest of his family was convinced he would be found not guilty. After all, Michael had an airtight alibi, and there wasn't a single shred of physical or forensic evidence that linked him to the crime. His brother, David, thought that finally the family name would be cleared once and for all.

“We were worried that without a trial we could never fully get closure in clearing his reputation,” says David. But when the jury returned their guilty verdict, the Skakel family was left shocked and devastated.

“It’s a feeling of disbelief,” says Stephen. “I love my brother and I believe in my brother 100 percent.”

And just this past week, the bombshell broke. "On the night of the murder, they picked up a golf club or some clubs from the Skakel yard ... and that they were going to get a girl, caveman style," says Kennedy.

*****

For nearly a year and a half now, Stephen Skakel spends every Saturday morning driving 60 miles from his home to Cheshire, Conn., to visit his older brother Michael in prison.

“Being able to see him face-to-face makes all the difference,” he says. “To let him know we’re still here and still fighting for him.”

At 37, Stephen is the youngest of the Skakel children. He was just 9 years old when Martha Moxley was murdered. Since the conviction, he has taken the lead in the fight to clear Michael and the Skakel family name: “There’s only so much people can take, and we’ve taken it for 30 years.”

Even more outspoken, however, is Skakel’s cousin, Robert Kennedy Jr.

“He doesn’t deserve to be spending 20 years of his life in jail for a crime he didn’t commit,” says Kennedy.

Although they were not close as kids, as adults, Bobby Kennedy Jr. and Michael Skakel shared a similar history – problems with addiction. Kennedy says he became close to Michael in 1983, when he first got sober. By then, Michael had already been sober for a year or two.

“I spent a lot of time with him, and we had a very, very strong relationship,” remembers Kennedy.

Kennedy spent six months investigating what he says were flaws in the prosecution's case against Skakel for the Atlantic Monthly article. He says he wrote the article for Michael’s son, Georgie: “He’s going to grow up with most people in this country thinking that his father murdered a girl, and he didn’t do it.”

*****

Kennedy says he received hundreds of letters after the article. One was from Crawford Mills, a classmate of Skakel's who told Kennedy that a friend, Tony Bryant, knew who killed Martha Moxley.

Bryant was one of the first African American students at Brunswick. Kennedy knew this could be a bombshell and located Bryant, now a businessman living in Florida.

"Tony's story has a lot of credibility and a lot of credence," says Kennedy.

Bryant told Kennedy that he was with two friends from the Bronx in Greenwich, Conn., on the night that Martha died. He said they went to Greenwich on several occasions, and that one friend became obsessed with Martha.

Bryant said his friends had a plan. They picked up golf clubs from the Skakel's yard.

"They said that they were going to go out and get a girl caveman style," says Kennedy. "And that Tony understood that girl to be Martha Moxley."

Bryant said he wanted no part of their plan and left. But when he read in the newspapers what had happened to Martha Moxley, he feared the worst.

"They never actually said that they had killed Martha Moxley. What Tony said to me - that he made it clear to them that he didn't want to hear about the details of what happened that night," says Kennedy. "But that they were in some ways boastful about it and were kind of egging him on to inquire to them about the details. They would say things like 'We accomplished our mission' and 'We did it.'"

*****

So why would he wait 28 years, until Skakel was convicted, to tell his story?

"What he said was that his mother, that he told his story immediately to his mother, that his mother urged him not to talk about it publicly," says Kennedy. "That was prompted by her fear that as a young, black man in Greenwich, he would be a target for prosecution."

Bryant denies any involvement in the crime. But when Kennedy located the two friends, he said neither of them seemed like they had anything to hide.

"I asked them to confirm some of the basic information, that I had heard that they were friends of Tony, that they had been to Greenwich with him on several occasions" says Kennedy, who received confirmation from the two men.

Kennedy didn't, however, ask them if they had anything to do with Martha's murder. But since the news broke this week, both men are well aware of the accusations against them, and have denied any involvement in the murder.

For his part, Tony Bryant admits he has a past conviction for burglary, and later had to shut down his company amid allegations of bad business practices.

Still, Skakel's legal team plans to see a new trial based on Bryant's story. And Kennedy remains steadfast: "Somebody decided that a Skakel was going to go to jail, and that all of the other evidence, the abundant evidence against other people, were going to be ignored."

*****

Kennedy now says these new developments support his arguments put forth in his original article - that the prosecution simply had the wrong man.

"The strongest piece of evidence is that Michael has an alibi," says Kennedy.

Skakel's alibi - that he was across town watching "Monty Python" when the murder occurred - has always been supported by several relatives, including his brother John.

“I took a lie detector test in which I was asked who was in the car that went to my cousins, the Terrians, who live about eight miles away,” remembers brother John, who says he convincingly passed the test. “And Michael was, in fact, in the car. That was my response.”

John’s 1975 polygraph results, however, were inadmissible in court. What was allowed into the trial, though, was the damaging testimony of two former Elan students: Greg Coleman and John Higgins.

The prosecution contended that 17-year-old Michael openly talked about the murder while attending the Elan school, where he was sent because of a 1978 drunk driving incident.

“Greg Coleman testified that he had heard Michael confess to having murdered Martha Moxley 5 or 6 times,” says Kennedy. “But when he came up in front of the preliminary hearing, Greg Coleman testified that Michael had only confessed to him once or twice.”

When Michael’s defense attorney, Mickey Sherman, asked Coleman why he had changed his story, Coleman admitted that prior to facing the grand jury, he had taken 25 bags of heroin. Coleman died of a drug overdose just before the trial. But a tape of his previous testimony was played for the jury.

Higgins, who Kennedy said was an Elan bully who tortured Michael at school, testified at the trial. Higgins, who refused our request for an interview, said Michael had also confessed to him.

"I think Michael could have gotten better representation," says Kennedy.

However, the worst day of all for the Skakel family and Sherman was the day of closing arguments.

“The prosecutors in the case used a very, very sophisticated multimedia technique at the end of the trial,” says Kennedy.

Prosecutor Jonathan Benedict transcribed and played Michael’s own words from his book proposal over gory photographs from the crime scene. “We needed to connect the dots and that’s what I did,” says Benedict.

The problem, says Kennedy, was that Michael was talking about being seen masturbating, not committing murder. “His tape-recorded words were used out of context by the prosecutor to imply that he was confessing to the crime. That multimedia display really convicted Michael in the end.”

*****

Before the most recent new information, the family was convinced that the family tutor, Ken Littleton, should have been looked at more closely. Littleton’s very first day on the job also happened to be the day Martha Moxley was murdered.

“He was rather an aloof individual,” remembers Stephen. “The first thing that stood out for me was his size. The guy was in good shape.”

At the time of the murder, both Littleton and Tommy Skakel said they were watching a movie together. But Kennedy says there were some inconsistencies in Littleton’s story.

“The accounts by various people of when certain things happened give enough leeway that Kenny Littleton could have been outside of the house at 10 o’clock,” says Kennedy.

"I wrack my brains as to what else is out there that we don't have," says Stephen.

What the Skakels now have, however, is hope. Tony Bryant has given a 90 minute deposition on videotape confirming what he told Kennedy. Defense investigators have also talked to the two men.

But why wasn't any of this new information known before the trial?

*****

Part III: Defense Seeks New Trial

(CBS) To Robert Kennedy Jr., the conviction of Michael Skakel was a miscarriage of justice: “This was the easiest case in the world to win. Reasonable doubt was all over the place.”

But it turns out that Tony Bryant's story was known even before the trial began.

Remember Crawford Mills? He says he first took the information to the prosecutor's office and Michael Skakel's trial attorney just before the trial.

"The prosecutor told him to get lost," says Kennedy. "They weren't interested in pursuing the new evidence."

Prosecutor Jonathan Benedict declined to talk about the new developments. But he told 48 Hours in April that he thought the trial was fair and appropriate. He also said that Kennedy’s article was wrong on all fronts – especially his attack on Littleton.

“He’s been diagnosed with having bipolar disorder,” adds Gene Riccio, Littleton’s attorney. “He’s had a number of hospitalizations. He’s a nice man who’s troubled and had a great deal of difficulty in his life ... I think arguments made that Mr. Littleton is responsible for this homicide are ridiculous.”

*****

Michael Skakel’s murder trial began on May 7, 2002. Benedict immediately went after Skakel’s alibi, which put him at his cousin’s house eight miles away at the time of the murder. For years, this alibi had never been in dispute, but Benedict began tearing it down by questioning a Skakel family friend - Andrea Shakespeare.

Shakespeare was one of the witnesses from the neighborhood on the night of the murder who was certain that Skakel never took that alibi ride. In her testimony, when asked if Michael had gone to his cousin’s that night, she replied he did not.

Benedict continued to attack Michael’s alibi – this time, using Michael’s own brother, John.

“He was considered to be the most credible alibi witness for Michael Skakel,” says Benedict. “But a funny thing happened over the years. When John came before the grand jury, he changed his story to this - he really didn’t have any recall of who went to the Terrians' house and who didn’t.”

Benedict may have succeeded in discrediting the alibi, but ultimately, he says Michael did himself in.

“The truth of the matter is that Michael Skakel couldn’t keep his mouth shut for a quarter of a century,” says Benedict, referring to those Elan students and others that Michael supposedly confessed to over the years.

“We presented 13 separate people who had separate conversations in separate venues with Michael Skakel, all of which were either out-and-out confessions or at least incriminating admissions by him. That’s how you try a circumstantial case. You put a bunch of facts together.”

But what Sherman failed to anticipate was the impact of Benedict’s closing argument.

“I don’t know if the Skakel family realized how many persuasive dots I had to connect,” says Benedict.

Up until that point, both sides thought Michael might be acquitted. “There were days when I thought ‘Oh, this is just never going to happen. This is just looking very bleak.’”

Benedict played a critical passage from Michael’s own book proposal to sum up his case. But the passage he used was edited in such a way that what the jury heard appeared to be a confession to murder: “And I woke up to Mrs. Moxley saying ‘Michael, have you seen Martha?’ I was like ‘Oh, my God! Did they see me last night?’ I just remember having a feeling of panic'."

But here is what Benedict intentionally left out: “And I remember thinking, 'Oh, my God! I hope nobody saw me jerking off.' And I woke up to Mrs. Moxley saying, 'Michael, have you seen Martha?' I was like, 'Oh, my God! Did they see me last night?'"

In August 2002, Michael Skakel was sentenced to 20 years to life for the murder.

Jeanine Pirro, a former judge and now New York's Westchester County district attorney, believes the chances of getting a new trial may be very good.

But she also says, "You have to look with some skepticism at a claim of knowing who the murderers are in a case where the people have agonized for almost three decades, and wonder what it is that brings you now to the public arena. Why did you not report this?"

There's also the question about Tony Bryant's criminal past - and other hurdles for the defense team. "This is all about weighing that delicate balance," says Pirro. "Do we open up the trial if we don't think there's any possibility of the verdict being changed?"

That's the dilemma the judge who presided over Skakel's original trial will soon face. "It's not beyond the realm of possibility for the DA to say we are going to look at this again," says Pirro. "No one wants someone who is innocent, wrongly convicted."

*****

Dorthy Moxley’s only daughter, Martha, would have turned 43 this year. “It doesn’t end. It really doesn’t end," she says. "Once you’re a victim, being a victim is just part of you forever.”

And while Bobby Kennedy understands her loss, he is steadfast: “I know he’s innocent. I know he’s innocent.”

“A skillful prosecutor can often put people in jail who are not guilty of a crime, and this occurs most often in cases involving notorious crimes or heinous crimes.”

At the same time, Skakel's attorneys are trying for a new trial. They continue to appeal his conviction. Among their claims: Michael should not have been tried as an adult for a crime committed when he was 15.

And, they also argue that Benedict’s multimedia closing argument deliberately misrepresented facts. The appeal will be heard this fall. Meanwhile, Michael’s family visits him regularly.

“He’s had a rough time in prison,” says Kennedy, who says the stress of prison is obvious. “I think the prison administration has given him a very hard time. He’s lost his teeth and he’s been told by the prison administration that he won’t be able to see a dentist for at least six months.”

As for the Skakels, they say this ordeal has actually made their family stronger.

“The positives are that we’re a lot closer together as siblings,” says John.

“What keeps me going is the hope that we’re going to get him out of jail back with his son,” says Stephen. “And not only clear his name, but all of our names.”

“It’s out there now,” says Kennedy. “I’ve done everything that I can do to tell the truth. And the result ultimately is in God’s hands, like everything else in life.”

*****

Michael Skakel's attorney, Hope Seeley, tells 48 Hours that she plans to file her motion for a new trial by the end of September.

Right now, Skakel's murder sentence runs until 2022 - with his first chance of parole at least 10 years away.

Skakel's wife has divorced him and she has custody of their 4-year-old son, George.

As for the Moxley family, Dorthy says she'd rather not talk about these latest developments until the motion for a new trial has been filed. But she says it's not the first time Skakel's lawyers have pointed the fingers at other suspects.

CBS Broadcasting Inc.