My celebration of the crash-free computer was a bit premature. I've had two of the worst crashes yet today, but at least it conclusively identified the problem for me - my computer just got around to informing me that the CPU fan is running too slow and failing. This is disappointing, but at the same time, as bad hardware goes it's just about as cheap to replace as it's possible to get, so I'm VERY relieved. I was afraid for a while I might have to get a new video card, motherboard or processor, none of which I can afford at the moment.
So it seems for the time being I won't be able to play any serious computer games. No Half-Life 2, no Portal, no Sims 2, at least until I can get a new fan installed. The system seems to run fine as long as I avoid taxing it with games.