I finally ended up taking it in to MicroCenter and the tech who examined it said the mother board is shot. He says he saw fried diodes on the back of the board.
The estimate to fix it would buy me a better replacement, so that is probably the route I will take.
It was a dual processor quad core (quad core dual processor? - whatever, it had eight) with maxed out memory, a heavy duty power supply and a pretty good graphics card. I will probably be able to reuse the graphics card, but memory seems to change type every other week, so that will be "stored". Heck, I'll probably keep the whole thing.
Before anyone suggests building my own, I do not have the expertise to choose the right parts to put something good together. I could assemble the parts myself, but I would be stuck if anything went wrong. I'd rather get something assembled that works.
The trouble is my budget is a bit limited right now.
Hopefully I can use my existing boot drive directly, but even if I can't the drive is still good and I can get the stuff off of it.
For now I'm using an old (slow!) Mac mini with minimal extras. It's OK, but I have gone too far down the PC path to switch over at this point.
Here's a link to a review with the specs of the PC. I have upped the memory to 9GB and swapped the graphics card.