Rachel Cox, who was slain in her D.C. apartment in 1983. A man is now on trial in her death. (Courtesy of U.S. Attorney’s Office)

It was New Year’s Eve 1983. Lynne Cox, then 18, was excited because it was the first time she was allowed to count down to the new year at a party with friends, instead of celebrating with her mother.

Earlier that evening, Cox’s mother, Rachel Cox, helped her daughter pick out the perfect dress. They sat in front of a mirror and experimented with different hairstyles, debating whether the teenager should have an up-do or let her hair drape over her shoulders, Lynne Cox told a D.C. Superior Court jury last week from the witness stand.

Lynne Cox called at midnight to wish her mother a happy new year, but the line was busy. When the daughter arrived home hours later, she noticed what she thought was a pile of clothes in the hallway of the Southeast Washington apartment. As she picked up a blanket from the top, she saw her mother’s body. “All I saw was blood,” she recalled.

As she recounted the horrific memory to the jury, Cox, now 51, began to sob and then hyperventilate. “I can’t breathe. I can’t breathe,” she cried as she rocked back and forth. Judge Robert E. Morin leaned over the bench and encouraged her to “be calm.” He ordered everyone out of the courtroom as federal marshals and the prosecutor rushed to comfort the witness.

More than 30 years after Rachel Cox was stabbed to death, authorities think they have finally caught the person responsible.

Prosecutors say DNA evidence found on Cox’s body ties a 58-year-old convicted sex offender, Joe Anthony Barber, to the killing. Even with that genetic evidence, though, they may have a difficult time proving their case. There were no witnesses and no sign of forced entry into the apartment.

Also, DNA of at least three men other than Barber was found in the apartment, lawyers said. The defense attorney told jurors that genetic material from an unknown man was found on boot laces used to bind Cox.

Prosecutors said a search of the apartment revealed DNA from two men who had dated Lynne Cox, but also genetic material from an unidentified man. It was not clear if that unknown sample is the one taken from the shoelaces.

Former U.S. attorney Justin Dillon, who is not connected to the case, said he thinks the trial is “winnable” for prosecutors but said any cold case has challenges.

“No witnesses to verify the story of either what led up to her death or how she was killed makes the case even more difficult for prosecutors, especially with the other DNA evidence present,” Dillon said. “But the defendant’s DNA inside the victim is still very strong evidence.”

After five days of days of testimony, the trial continues this week.

The breakthrough in the case came in 2013, when police arrested Barber, then a warehouse laborer, and later charged him with multiple offenses, including first-degree felony murder while armed. When the slaying occurred, he lived just a few blocks from the Cox apartment. Barber was later convicted in the rape of a 10-year-old girl and spent 19 years in prison.

Prosecutors say Barber raped Rachel Cox, then stabbed her 12 times. DNA from fluids found on her body identified Barber as her attacker, authorities say. Although DNA tests were conducted in 1984, the technology was less sophisticated then and didn’t lead to an arrest. So in June 2013, the evidence was retrieved from police archives and retested using modern techniques.

During police interviews before he was charged, Barber repeatedly denied knowing Rachel Cox, who was 43 when she was killed, and gave detailed accounts of his whereabouts on New Year’s Eve 1983. Such vivid detail struck detectives as odd, prosecutors told the jury. And denying he had any type of relationship with Cox, even though his DNA was found at the scene, also seemed suspicious to detectives.

Once Lynne Cox was able to compose herself on the witness stand last week, she slowly described to the jury the moments after she found her mother’s body. Cox said she first telephoned her mother’s best friend for help. “My mommy is on the floor,” she remembered screaming in the telephone. The woman told her to feel her mother’s wrist to see if there was a pulse. There was none.

Cox then telephoned 911. She collapsed onto the kitchen floor with the phone cord wrapped around her until police arrived. “I begged the operator not to hang up and to stay on the phone with me. I was so scared,” she said, sipping water and taking deep breaths.

Rachel Cox had been employed as a personnel department supervisor for the District’s Public Defender Service. Friends who testified during the trial described her as hardworking and said she often kept to herself. Cox could have attended a New Year’s party thrown by the office’s former chief, Charles Ogletree, now a professor at Harvard Law School. But she told friends she would stay home that night.

When Cox was killed, concerns in the city surfaced that someone connected to her job may have been responsible. But there was no such evidence, and the case grew cold.

During the trial last week, prosecutors acknowledged that DNA of other men had been found during the investigation. But they emphasized that only one male DNA profile was found on Cox’s body: Barber’s.

Barber attorney Joseph Caleb told the jury that his client’s DNA “does not mean he raped or killed” Cox.

During his opening statement, Caleb told jurors that another man’s DNA was found on boot laces that were used to tie Cox’s hands behind her back.

Barber’s various statements to homicide detectives, Caleb said, were fueled by Barber’s fear of being interrogated at homicide headquarters for a crime he did not commit.

Still, what remains unclear is whether Barber was now suggesting that he had a consensual relationship with Cox, who was nearly 20 years his senior. Lynne Cox and two of her mother’s friends testified that they knew of no relationship between Barber and Rachel Cox. But the defense suggested that if Rachel Cox was seeing a younger man, she may have kept it secret.

Barber’s attorney insists that his client is innocent. “Joe Barber did not murder or rape Rachel Cox,” Caleb said.