What a mess. So, after the misadventures with the first repair place, I took it to another. After a week, they called to say it was ready. Of course, it wasn't; it was having the exact same problem. So today was another week later, and this time they said it was the memory that was bad, intermittently. Okay, fine. The replaced the RAM, and I tried it out in the store; it booted, but kept getting some sort of page fault when it tried to shut down. But at least it was booting, so maybe they were on to something.

I have it home now, and it's connected to the internet, so I'm a tiny bit satisfied. Everything seems really sketchy, though; I think there are problems with the registry. So, I'm in the process of uninstalling everything. Now the wireless card has stopped working. Anyone know any good diagnostic software?