I finally fixed my Windows XP screensaver problem. The short story is that the screensaver doesn't work -- it just never starts -- so I resorted to either starting it manually (right-click on the desktop, choose Properties, choose the Screen Saver tab, click Preview), logging out, or turning off the monitor.

After reading a few possible solutions here and there that said PowerDVD might be the problem, I finally just went ahead and deleted PowerDVD, and a minute later the screensaver started working. (It really was a minute. I forgot that I had it set really low when I tried other things to make it work.)

If you actually use PowerDVD you might want to make sure you can re-install it, but in my case I don't use it, so deleting it was no problem, and it was a pleasure to see the screensaver come on automatically.