Okay thank you everyone very much for your suggestions. I have tried most of them. The problem was the video card was truely damaged (it was old and had a hard life of constant 3D gaming for probably 3 years or more).
I was getting obvious, visible, screen glitching, even during the POST, before any boot options are available. So I put in a known good PCIe card and booted the computer with that with safe mode enabled so as to remove the offending driver, thinking this was the cause of Windows XP not booting. However, a few seconds after choosing safe mode, even after hitting F8 and telling the computer not to restart on errors, the computer restarted, and looped, whether safe mode was enabled or not. So then I suspected the hard drive was also corrupted. ---related to the video card going bad?--- so I booted from a retail XP disc and went into the Recovery console. From there I did a simple "chkdsk /r", which took forever to complete: many hours. However when it was done, the computer went right into safe mode no problem, I removed that corrupted driver, restarted the computer using the on-board graphics and had Windows up and running.
Now I'm doing some low-level hard drive error checking stuff booting from a CD. I'm concerned that the hard drive is failing.
I'm sorry I'm such a noob but I've never had safe mode just not work. I also feel like a noob because I don't know whether or not it's possible for a simple driver to go bad, and actually destroy data on the hard drive that would cause SAFE MODE not to work. Maybe the two problems are unrelated? Maybe safe mode hasn't been working for a long time on this person's computer.