Oh, the headaches.
Anyways, I'm finally sending it in under warranty to hopefully be fixed. ATI lists a number of things that should very likely be serviced. I hit three out of four...
Now, I'm debating three options:
1) Get my old computer back up to snuff, so I can still come online
2) Buy a new, cheap videocard that will hopefully work in this machine, and return it when I get my old card back. Morally questionable, this one. ;)
3) Take approximately a three-week vacation from the internet.