Does it also turn off monitor if you boot to winXP in safe mode? What kind of monitor you have been using?

Was this a clean reinstall of windows?
If your screen is ok during the setup screens and the XP load screens and shuts off at teh desktop sounds like driver issue or its set to a resolution the screen doesn't support.
If you boot into safe mode can you get the desktop? and if you can try deleting the adapter in Device manager and seeing how it goes using just the standard vga driver

Now, it won't start up and the DVD_ROM won't open when it is powering up. I push the button, and I hear the mechanisms move, but it doesn't open. And, the last time I watched the POST, it listed the CPU as the wrong speed; much lower than it really is.

EDIT: Just tried it in Safe Mode, and while working on it, the system just turned off. It's most likely a power supply issue at this point

Gazirra wrote on 2020-03-22, 19:35:

the DVD_ROM won't open when it is powering up. I push the button, and I hear the mechanisms move, but it doesn't open.

This is probably unrelated to the main problem. you should open that dvd and clean it properly.

Gazirra wrote on 2020-03-22, 19:35:

And, the last time I watched the POST, it listed the CPU as the wrong speed; much lower than it really is.

is the cpu frequency setted up correctly? I had an old athlon xp that would do similar things on low freq. Try to take out the battery fo a while to clear cmos and then enter bios.

I reset the CMOS and reinstalled the proper GPU drivers. System is now up and running normally.
Gonna clean out that DVD now.

EDIT: Alright, cleaning the drive is a bit beyond my immediate knowledge. Luckily, I had a compatible IDE drive floating around.

So, it was working fine for a time. I had reinstalled the original graphics card, a functioning IDE DVD drive, and I had it working for nearly an hour straight.
I then tried to install a new graphics card and upgraded the RAM. The new card is a Dell Genuine ATI Radeon HD 4450. I had it working for awhile, sitting on the screen saver, which didn't work at the time of the first post of this thread.
I then moved it to where I had it last prior to all the current problems. When I had moved the system, it went back to shutting down randomly

Get a decent PSU like seasonic 650W, get GTX 7900 GTO which will not break your older games this way. I'm waiting for parts to finish my XP computer as well for this purpose.

Cheers,