Have you tried booting with an absolute minimum of programs loading at startup?
I tried it, but with no success.
However, persistence pays off! I narrowed the problem down to the Graphics Display device. Removing and re-installing it, didn't help. I have the latest drivers for it, and they don't help. I checked the computer using Aida32, and found there were 2 graphics controllers, and 2 graphics accelerators installed. This condition had existed for a long time, and was only now giving a problem. I checked the computer physically, and found a graphics card, which I had forgotten about, as well as the built-in chip for the graphics controller. I removed the card, and the problem went away. Everything seems to be working now.
Thanks, everyone, for all your suggestions.
Tom