I put in a used 8600GT from eBay that I thought matched the old card, and now it continues to stay powered-up, so...
Problem#1 - Dead video card. FIXED.
Problem#2 - No signs of life other than the fans. FIXED
I figured it was a dead mobo and was about to plunk down $400 for a new one, but then I decided to play with the RAM. It's a two slot DDR2 config, and comes with 2, 2GB Kingstons. The long and short of it is, both sticks seem to be good, and both SLOTS seem to be good, but if both are in at the SAME time it won't boot. I found a 1GB stick in my stash and am booting with 3GB instead of the 3.5GB or whatever Windows XP uses.
Problem#3 - "HUC Shutting Down". PENDING
The main display now boots. The screen shows mostly ASCII dollar signs "$", and then I see the XP boot progress bar. I see the logo, then eventually the right player (5" display) shows the Windows: Add New Hardware Wizard. I've got a few seconds at this point. The trackball responds, and I can click one of the buttons to simulate a mouse click, but no matter what I do it'll eventually disappear and display "HUC Shutting Down", then reset. I imagine this is because my replacement video card isn't an exact match.
I'm pretty sure the solution is to buy the new "flash" drive and video card combo from PokerTek, but instead of paying $250 I bought the card on eBay and the new drive from Milton187 for less. I'll update the thread when the drive comes in.