Dr. Conrad Murray believes he can still PROVE Michael Jackson injected himself with a fatal dose of Propofol -- and now he's begging an appeals court to let him test his theory.

Murray's lawyers are filing a new motion in his appeal -- claiming a vial of Propofol could hold the key to his innocence ... if only a judge would allow forensic testing to search for traces of lidocaine.

The lidocaine is important because the prosecution argued that Murray hooked MJ up to an IV bag containing the fatal dose of propofol and left him alone ... but first, mixed the Propofol with lidocaine to ease the sting of the drug.

Murray claims testing will prove there was NO lidocaine on the vial ... because Jackson injected himself with a pure dose of Propofol ... and killed himself.

Murray -- who was found guilty of manslaughter and is currently serving time in L.A. County Jail -- has already made two requests for testing. Both were denied by the judge who presided over his trial ... and ruled that Murray should have made the request BEFORE the trial began.

Murray's team will file the motion in California later today. It could take months before the court makes its decision.

Dr. Conrad Murray -- the man who killed Michael Jackson -- believes he is the one man Katherine Jackson can turn to for some honest advice ... and has invited MJ's mom for a jailhouse conversation.

Murray released a statement through his lawyers to CNN ... saying, "I've been told that she has a desire to speak with me before she departs this life."

"Seeing that she is up in age and in questionable health, and the fact that she is the mother of a very dear departed friend, it would give me great pleasure to sit with her one on one and answer any questions she might have."

Murray continues ... "I do not want Mrs. Jackson to suffer. She remains as dear to me as my own mother, unbeknownst to her."

Conrad claims he's not allowed to follow the news as closely as he'd like to in jail ... but is aware of the family drama ... and says Katherine appears to be "extremely sad."

"I also heard she is having a difficult time."

Murray says he's listed Katherine on his jailhouse visitor's list in case she wants to take him up on his offer. So far, no word on how Katherine feels about the situation.

Dr. Conrad Murray is pulling a Floyd Mayweather Jr. -- pleading with a judge to spring him from L.A. County Jail because it's taking an extreme physical toll on his body ... and if he doesn't get help soon, Murray believes he'll DIE behind bars.

But here's the crazy thing -- unlike Mayweather, Murray's not asking for house arrest (he knows that will never happen) ... Murray's asking to be sent to PRISON, where he believes he'll get better care.

Murray's lawyer tells TMZ, he wants to serve out his time in the big house because he's being treated like filth in L.A. County jail -- getting fresh air once a month, and fresh underwear once a WEEK.

As a result of the alleged deprivation, we're told Murray's health is failing -- his hair, nails, and skin are gnarly  ... and he's been suffering from a constant headache over the last few weeks.

Murray says he's never gotten headaches in the past -- and is worried it might be a brain tumor.

We're told Murray asked to see a doctor, but got shuffled around and has received no medical attention.

Murray told his attorney, Valerie Wass, "I may not make it out of here alive. This is a very dangerous place. I'm in here dying. The system is intent on killing me."

A rep for the L.A. County Sheriff's Department tells us, the department doesn't comment on pending cases.

Conrad Murray doesn't regret for a second doing the documentary that infuriated Judge Michael Pastor, because he wanted the public to hear his side of the story.

Murray -- who declined to testify in his trial -- spoke with friends and family after the sentence.  We're told Murray said he knew he was going to get the maximum sentence, so it didn't bother him that he became Judge Michael Pastor's human punching bag over the things he said in the documentary -- in particular, trashing Michael Jackson and not accepting any blame for his death.

And we know more about Murray's reaction to the sentence.  He's saying he's "surprisingly upbeat" about the sentence, telling one friend, "I'm just relieved it's finally over," adding, "Don't worry, I'm fine, and I'll be out soon."

Dr. Conrad Murray's baby mama Nicole Alvarez is furious over the maximum sentence that was imposed today -- claiming Judge Pastor's decision was "ridiculous."

Nicole stepped out today with her son -- insisting Murray has beaten himself up non-stop since Michael's death ... despite Judge Pastor's claim the doctor showed no remorse for his crime.

Nicole adds, Murray has been "mournful for the past two-and-a-half years."

Conrad Murray's lawyer J. Michael Flanagan admits the decision to do a tell-all behind-the-scenes documentary was "probably a mistake" ... but tells "TMZ Live" the Doc really needed the money.

Katherine Jackson wants Conrad Murray to rot behind bars -- telling reporters outside the courthouse, the doctor's 4-year sentence is "not enough."

Speaking to KTLA ... Katherine added, "Four years won't bring my son back" -- but she admits ... Judge Michael Pastor was extremely fair with his sentencing.

Conrad Murray's defense attorney J. Michael Flanagan just stormed away from a news conference -- after he was ambushed by hecklers.

Flanagan was in the middle of making a statement, claiming, Murray "led 56 years of exemplary life" -- at which point he was interrupted by someone in the crowd ... "And then he killed Michael Jackson."

Flanagan asked for the hecklers to be removed ... but after nothing happened, Flanagan said, "I'm out of here."

Judges, prosecutors and criminal lawyers who have spoken with TMZ agree ... Conrad Murray should not get the maximum sentence -- 4 years in prison -- but the fact that he killed Michael Jackson changes everything.

It's not supposed to be this way -- the fame of the victim should be irrelevant -- but it's hard to ignore the fame of the victim.

The people we spoke with say the typical sentence for someone in a similar position -- no criminal history, an otherwise unblemished record -- would be a "blended sentence" -- a year or 2 in jail, and then a year or 2 of community service. 

Judge Michael Pastor made it clear when he denied Murray bail -- he views the crime as extremely serious, possibly telegraphing a maximum sentence.  It's hard to tell what Pastor will do, but almost everyone considers him a fair but stern judge.

The fact that the D.A. is asking for $100 million in restitution shows how much of a difference it makes that MJ is the victim.  The reality is  -- in terms of money -- Michael is worth more dead than alive, so there should be no restitution.  His 3 kids will now get hundreds of millions in a windfall.

Here's the reality ... Murray will not serve a day in prison.  Because of a new California law, any time he gets will be served in L.A. County Jail, and the amount of time will automatically be cut in half.  And, Murray would be eligible for house arrest.

Katherine, Jermaine, and Rebbie Jackson just arrived at the L.A. County Courthouse -- moments before Dr. Conrad Murray is scheduled to be sentenced.

La Toya Jackson just showed up with Kathy Hilton ... Randy Jackson rolled up minutes later.

So far, no sign of Joe.

English was not the only language used in the jury deliberation room in Conrad Murray's case ... this according to a relative of one of the jurors ... and there may have been a language barrier in the juror room.

We're told at least 2 of the jurors began discussing the case in Spanish during the 8-hour deliberation. 

A relative of one juror -- we'll call him juror A -- tells TMZ ... another juror -- juror B -- had "some trouble" understanding some of the testimony.  During the deliberations juror A had to translate the testimony into Spanish to juror B.

In the questionnaire jurors were required to fill out, the first question read, "Do you have any difficulty reading, speaking or understanding English." 


A spokesperson for the court tells TMZ ... no juror ever requested a court-appointed translator at any time during the trial or deliberations.