Thanks to those that responded to this post. I did try a known good
power supply, with no success. I also tried resetting the CMOS, but
would that matter? Even if the battery is completely dead, the
computer should still boot up with default settings, right?

Right. But if the battery wasn't dead, and somehow the CMOS was corrupted, or
"confused", and saving that condition, a reset might have cured it. It was a
long shot but easy thing to try...

The other thing to try is to disconnect everything and pull all cards, and try
to boot. Add video back first, and then add things back until you find
something that causes the problem. If the problem still exists with minimal
devices connected then its something onboard the systemboard, and your screwed.
If its a device, replace it.

Dale