Ha! CC_333 wins the prize! Monitors shows only 1024x768 as an option, so even if it's not the sleep problem, I definitely need a driver update.

I know USB devices can cause the problem, in particular my thumb drive, but I've already dealt with that one, so I'm pretty sure it's the video card.

Update: The driver in question is called the Apple NVIDIA Driver and it was published by Apple. Apple NVIDIA Driver 3.0 v1.1 (Apr, 2002) can still be had from Apple's website.

http://support.apple.com/kb/DL1150

Update 2: The installer won't run on my machine, however.