Definitive Update:

It was the MoBo. Yesterday while playing, the main system crashed again with a nasty-sounding POP. I smelled a little smoke. Yeah. So I starting pulling things and trying to get the motherboard to POST (which it never did). I was doing all this with a good power supply, too. Turns out the one I had in the case is NOT defective. Anyhow...

I got down to just the memory and the processor in the MoBo. Pulled those two parts as well. Reset CMOS (for about the fifth time). Powered up. No POST. The MoBo is dead. The other parts look good. I'm on my way to pick up the new motherboard. We're going to see how it does.