Well, the problem just got a lot worse apparently.
I was going to start a benchmark run of 3dmark11 (free version) just to see what would happen/check for artifacts/etc.
Well, once I clicked start my monitor turned off. At first I thought the test for some reason did this, but the monitor did not come back on. Restarted the system, and nothing showed up, no POST.
The computer seems to be operating OK otherwise, but obviously I can't really tell. The first time I was able to shut down the computer with the keyboard, so Windows was still running and responding.
I can try a different video card tomorrow probably, but I am assuming the most likely explanation here is that my card just fried itself? I hope not...