Thanks for all the help so far, everyone.
So this laptop didn't come with a recovery CD, evidently, and after it started having problems, I went ahead and activated its recovery program to restore from the factory install off the partition. The end result - no improvement; exact same problem. (This was before I had run Malwarebytes and found those weird registry keys.) It makes me think maybe there was something wrong with the factory install to begin with, like Tarrant had suggested. I know it's unlikely, but I don't know what else could be the culprit.
In any event, he's taken it out for a bit, so I can't work on it at the moment, though I will post back later. But while he's away, I've got to ask - what's bad about Norton IS 2009? I'd heard over on the security forum they got rid of a lot of the bloat and that it had good detection rates. (I ask partly because I'm running it on two out of my three machines. 🙂 )
In any event, I will post back in a bit once the laptop is back and I can work on it some more. I really appreciate all your help, guys!