(CNN)A Louisiana judge ruled Monday that Robert Durst, the millionaire real estate heir charged with first-degree murder, will be held without bail. That's no big surprise. In 2001 -- the last time he was accused of murder and released on bail -- Durst fled to Pennsylvania, where authorities caught him after he tried to shoplift a sandwich from a supermarket. As the attorneys sparred in court and witnesses testified Monday, they revealed new details about the investigation that led to Durst's March 14 arrest, and set the stage for what will surely be a fierce legal battle. After the hearing, Durst's attorney, Dick DeGuerin, spoke with CNN's Jean Casarez. Here are some key details from Monday's hearing and the interview: . Durst, who appeared in court wearing an orange prison uniform and shackles, was arrested after federal agents tracked his cell phone, according to information presented in court Monday. Investigators knew he'd left his Houston condo with five suitcases on March 10. And, since a warrant allowed them to track his cell phone, they saw when it pinged a tower 85 miles east, in Beaumont, Texas. But suddenly, he had stopped using it. Investigators thought the trail had gone cold. "They had no indication of his movement," said Jim O'Hearn, an investigator for the Orleans Parish district attorney's office. But then, authorities tracked him to New Orleans after he called his voice mail twice from a Marriott there, O'Hearn testified. That's where FBI agents found and arrested him. Last week, court documents revealed Durst had a loaded .38-caliber revolver, 5 ounces of marijuana, his passport and birth certificate, a neck-to-head latex mask with salt-and-pepper hair attached and more than $40,000 cash, mostly in $100 bills. Among his possessions, he also had a UPS tracking number. The package was later intercepted by the FBI, prosecutors said in court Monday. It contained clothing and more than $100,000 in cash. It's a case Durst even has made himself. In "The Jinx," the HBO documentary that featured him, Durst said: "You can't give someone charged with murder bail because they're going to run away, of course. Goodbye, $250,000. Goodbye, jail. I'm out." In a seconds-long news conference after the hearing Monday, Durst attorney DeGuerin said he had no hope for bail and the judge's decision was not surprising. The legal team, however, did obtain "a lot of information," he said, and a preliminary hearing was set for April 2. "All in all, I think this has been a very good day for us," he said on the courthouse steps. He walked off without elaborating. DeGuerin cast doubt Monday on the validity of the Los Angeles arrest warrant that led to Durst's detention, and argued that items found in the hotel room search shouldn't be admissible because detectives may not have had a search warrant at the time. He also said a detective and prosecutor interrogated Durst for three hours without his attorney present. Since the weapons and drugs charges Durst faces in New Orleans are based on what investigators say they found in his hotel room, this is likely to come up again. But prosecutors argued that the matter at hand Monday was whether he is a flight risk or a danger to the community. The judge sided with the prosecution Monday. But this is just the first step in what will likely be a lengthy legal battle. "As long as Louisiana wants us here, well, we'll stay here. We'll fight," DeGuerin said Monday. But the bigger courtroom fight will likely unfold in Los Angeles, where the district attorney filed a first-degree murder charge against Durst last week. Durst awaits extradition to Los Angeles to face that charge. If convicted, he could face the death penalty. Prosecutors accuse Durst of "lying in wait" and killing Susan Berman, a crime writer and his longtime confidante, because she "was a witness to a crime." Berman was shot in the head in her Beverly Hills, California, home in December 2000, shortly before investigators were set to speak with her about the 1982 disappearance of Durst's first wife, Kathleen McCormack Durst. Robert Durst has long maintained he had nothing to do with Berman's death or his wife's disappearance. "I just don't think that they had sufficient evidence to have him arrested," DeGuerin said Monday. "They had a lot of suspicion. They've always had a lot of suspicion. And that television show just added to that suspicion." It's not the first time Durst has been accused of murder. He admitted to killing and dismembering his neighbor in a 2003 trial, but he was acquitted after arguing he acted in self-defense. FBI agents have also asked local authorities to examine cold cases in locations near where Durst lived over the past five decades, a U.S. law enforcement official said. On Monday, police said there was a connection between Durst and a college student who disappeared from Vermont's Middlebury College in 1971. In response to a question at a Tuesday news conference from CNN, Middlebury Police Chief Tom Hanley said: "There's nothing in the files to indicate (Durst) was questioned" at the time of her disappearance. "We don't know if they ever had any personal contact," the chief added. The connection in the case was one of proximity, Hanley said. Durst owned a health-food store in Middlebury, and Lynne Schulze was last seen across the street from the store near a bus stop. She had purchased dried prunes from the store earlier. DeGuerin brushed off the accusation, saying that his client "may have been in Chicago when Jimmy Hoffa disappeared." Other cases in upstate New York, the San Francisco Bay Area and Southern California are also getting a new look. Durst was placed on suicide watch, according to police, but DeGuerin said last week that Durst needed to be in a hospital setting, not because of the possibility of suicide, but because he has serious medical conditions. The 71-year-old is suffering from hydrocephalus, which required brain surgery a couple of years ago, DeGuerin said. Doctors implanted a stent on the right side of his head, the attorney said last week. "At the same time he was in the hospital he had an operation on his esophagus to remove cancer. So he's got some serious health issues. ... He's lost a lot of weight. He's not in good health," DeGuerin said. Durst appeared in court Monday with his head shaved, the stent prominent. DeGuerin also said that Durst is "mildly autistic" and has received treatment in the past from one of the country's leading experts in Asperger's syndrome and autism. "He's quiet and he's reserved and he's actually bashful. But he's always been looked upon as a little bit odd," DeGuerin said. "And what we discovered 15 years ago was that he's autistic, mildly autistic, but it explains a lot of his, what others look upon as unusual or bizarre behavior." But DeGuerin said his client's health struggles don't mean he's incompetent to stand trial. And DeGuerin said they're eager to go to court and fight the accusations against him. "He's a little frail and he has some memory problems sometimes," DeGuerin said. "But he's not incompetent." CNN's Anne Woolsey, Amanda Watts, Jean Casarez and Ray Sanchez contributed to this report.
Police chief in Vermont says Robert Durst owned store where college student bought prunes before she disappeared . Durst's attorney: "I just don't think that they had sufficient evidence to have him arrested"
Robert Durst, who is charged with first-degree murder in California, awaits extradition .