While I would have been furious, she was completely okay with it. She calmly told me, "The person who stole it clearly needed it more than me."
Now, this isn't to say that stealing is okay. It's certainly not, and I'd be pissed. However, this person knows what he did was wrong. He really seems to hate what he had to do to get the computer. But he clearly needs it. Maybe he wants it so he can get a job, or wants it so his kid can succeed.
Try appealing to this side of him. Find out why he needs it. I doubt it's so he can watch YouTube videos, based on his email. You can buy a cheap desktop (or even laptop) for a few hundred dollars. Offer to trade a crappy computer for yours. (I doubt he wants you to buy it back; he seems to care more about the computer than money.)
The person almost definitely doesn't need a computer as good as what you had stolen from you, and he's already feeling really guilty about it. And, if he agrees, you can try to find out who actually stole it and tell the police.
Sure, it's unfair you'd have to drop a few hundred dollars- but consider it a donation. (Depending on the circumstances, you might even be able to figure out a way to legally donate it to him through some sort of organization- which would be tax deductible.)
After all, giving him a computer could change his life. Think about how much your life has improved by merely owning a computer; something most people on HN take for granted. You could turn a bad situation into one you're really proud of.