But life hasn't always been such smooth sailing. In fact, Laura says she spent two decades living in fear as a victim of rape. Correspondent Susan Spencer reports.
"It's really devastating. I mean, it's something that just completely overshadows your life. And it's not something that you ever recover from fully," says Laura.
It's been almost 20 years since that horrible night when she was attacked. Laura, then 18, had just moved out of her parent's home in Baltimore. With dreams of college and a career, she was ready to take on the world.
On Oct. 14, 1983, Laura says, she fell asleep watching television. She says she heard a noise while she was asleep, but she thought it was her roommate returning home.
"It sounded like a shuffling noise in the background," she recalls. "But then, of course I was awakened, and without going into too much detail, I did wake up to a gun to my head and a pillow over my face."
According to the police report, an intruder entered Laura's apartment through her roommate's window and forcibly raped the frightened teenager in her own bed.
"It was fear, it was shock. I was certain that there was a really good chance I wouldn't live through it. I really thought I might die," she says.
She didn't see her attacker, and she says she didn't struggle during the attack: "You know, if I could change one thing, looking back over the years, feeling like I'm strong and capable of taking care of myself, I would have fought. But in fact, I didn't."
So why does she have second thoughts about it? "It's really a life sentence to be raped," she says. "It's always vivid in your mind."
When police came to investigate, Laura immediately sensed something terribly wrong. The detectives seemed to doubt her story, thinking perhaps she'd known her attacker - and only decided after the fact that this was rape.
"All the responding officers that night had been males. And a female came in and really it started to look like an interrogation," recalls Laura. "It became quite clear to me at that point that they definitely did not believe this had happened."
But far worse than that, she says, her own family didn't completely believe her, either: "The response was, we believe something happened. But our perception and our perspective on it is really based on what the police department told us … We believe that maybe it was someone you knew or what is commonly referred to as date rape."
Laura was shocked by their reaction. "Always believe your children and support them," she says. "Even if it's really difficult to do that."
Laura's mother would not talk to 48 Hours about the case on camera. Her younger brother, Stuart, who was a teenager at the time, says no one in the family wanted to talk about what had happened then, either. It was too overwhelming.
"I feel that she didn't get the support that she wanted or needed, because I don't think that some people in the family knew how to deal with it," says Stuart. "It was just a very tense situation."
But Laura never wavered. A total stranger had raped her, and she kept after the police, who did little, noting on one report that the "solvability" of this crime was "poor."
In fact, the police may not have been trying very hard. And a curious note in her file suggests why - claiming that because of family stress, she actually wanted the case suspended.
"It's actually offensive to me that I would suggest that I'd want them to drop the case," says Laura. "I mean, it never occurred to me that they wouldn't be able to solve the case."
As the years passed, and nothing happened, Laura felt under siege, fearing her attacker might return.
"I moved in with a roommate, and I always had roommates because I would never live alone," she says. "I didn't know who this person was. So it was really the dark shadow sort of lurking, near the house. For me, having everything locked and a security system was probably the best level of security I was going to get."
Nineteen long years after Laura was attacked, she saw a news item that literally would change her life. It turns out that she was by no means the only victim of an unsolved rape in Baltimore. The city police department had more than 4,000 rape kits simply sitting on the shelf, and a new cold case unit was about to re-analyze them.
Determined that hers should be first, Laura picked up the phone: "I called them and said, 'Look, I'm not kidding. I'm going to call you every day.' And finally, I got the name of a detective who might be able to help me. His name was Bernie Holthaus."
"One of the first questions I asked her, I asked her what she was wearing," says Det. Bernie Holthaus, the lead investigator of cold cases for the Baltimore sex crime unit. Laura says she told him, in a split second, exactly what she was wearing.
Then Holthaus says he asked her how this attack affected her lifestyle over the last 18 years.
"It's difficult to trust people or get close to people," recalls Laura. "I explained that I'm not married. I don't have children. And you know, a lot of that has to do with letting people get close to me. And for personal reasons ,I really feel like I need to have this solved."
Finally, after that conversation, someone was listening. More importantly, however, someone believed her. But Laura says she was advised not to get her hopes up.
Detective Holthaus and his partner Chester Norton had no idea what they wouldn't find, until they started digging up the old evidence. They first discovered that the rape kit, all the critical DNA evidence gathered during the initial investigation, was gone.
"No one knows how it got lost, but Laura's rape kit was gone, missing from evidence control, no DNA to help solve this case, " says Norton. "It was an obstacle. And we both looked at each other. And we thought, 'OK, we don't have this. What do we have?'"
All they had were a few fingerprints, and they turned to the state's gigantic database – which includes more than 1.8 million prints.
The crime went unsolved for 19 years, but it took less than an hour to match the fingerprint.
"I was ecstatic for probably 30 seconds. But then it started to change because I knew that we had a lot of work to do," says Holthaus.
The print matched one from 50 year-old Alphonso Hill, a career criminal who'd been in and out of jail since 1975 - and was out at the moment.
But after nearly two decades, can the detectives finally end it? Can they at last catch the man who raped Laura Neuman?
"Knowing we missed him by 10 minutes the first night was discouraging because you're wondering is he out there doing this again," says Norton.
Amazingly, they had a suspect in just three days. "It was just an incredible, incredible, collision of emotions that I was experiencing," says Laura.
They caught up with Hill in a psychology class. He says he was back in school, trying to turn his life around. The attack on Laura Neuman, he says, never even occurred to him.
"He knew we had some evidence. He didn't know how much or how little we had," says Norton. "But he knew we had a good feeling that we know he did the rape."
In fact, with only fingerprints, the detectives desperately needed a confession - and they had one shot. They threw three Polaroids of Laura Neuman on the table.
"I told him I matched Laura with him. That's what you caused her," says Holthaus.
"I would never have dreamed she had suffered that way, for that long, no," says Hill. "And then that's when I was ready to let it go. And I was ready to get it off me."
The detectives were stunned. Hill described the rape in intimate detail: "None of it was pre-meditated. I just needed money. I was kind of –I guess, drugged up. And I just went out on a prowl for an easy entrance to an apartment. I mean, it was all just random."
Hill claims he'd felt guilty for years. "It was gonna continue to haunt me. I was tired," he says. "I was ready to get it over with. I was glad to be caught. I wish I had been caught way back then."
After all that waiting, it seemed so simple. Five days after re-opening the case, the man who had haunted Laura's life was behind bars.
"I felt like celebrating. I felt freedom. I felt vindication. I felt justice. I mean, it was just an overwhelming experience," she says.
But as it turns out, there was no good reason why Alphonso Hill couldn't have been picked up much sooner. The fingerprint database had been up and running since 1991, and Hill's prints had been in the system for years.
"My feelings about the police department are that yeah, they really mishandled me as a rape victim in this case," says Laura, who says that only her dogged persistence solved this case. She never wavered in her story to police, or to the family who doubted her.
"You know, my mother was the first one to pick up the phone and call me to say, 'I'm really sorry that this happened.' She apologized," says Laura. "But it was tempered by her explanation that the reason she didn't believe me was because the police didn't believe me."
By last September, there was no doubt. Seeing him for the first time in the courtroom, Laura glared at Alphonso Hill as he pled guilty to raping her.
"I was just hoping she was able to feel that I was sincerely sorry for what I had done in every way possible," says Hill.
"I said I have lived 19 years of hell," says Laura. "And I've lived in fear because of what you did. And I said, 'I'm really angry about it. And I don't want to be angry anymore.' And I said, 'Thank you for saying your sorry and taking responsibility for it. I hope I can eventually get to the point of forgiveness.'"
Hill was sentenced to 15 years. Laura's moved on and she's determined not to be a victim. She's newly engaged, and she's trying to mend hurt feelings with the family.
"I think I'm doing great. I mean I have a wonderful life," says Laura. "I feel grateful for the outcome and I feel thankful for the life that I have."
What happened two decades ago has given her a new purpose in life.
"I want the perception of this crime to change," says Laura. Last May, she launched a foundation to spread the word that old cases can be solved.
"The idea for the foundation is really to get people to come forward and go to their local police departments to push to have their cases re-opened," she says. "And to push to re-examine the estimated 500,000 rape kits gathering dust in evidence rooms across the country."
"It is all around us. It is happening every day all around us to people that we know. And no one talks about it. And until we start to talk about it, it will not change."