Sounds like problems with DirectX and/or the graphics card drivers. Try up[censored] gfx card drivers for starters.
 

I have the newest drivers. Also I've tried three older ones without any change.

I've also reinstalled DirectX a couple of times. I have the same problems in Baldur's Gate II (which uses OpenGL) when using 3D acceleration.

Looks to me like it might be your video memory playing up. You haven't tried to overclock it lately have you?
 
This will be caused by a video card failing to respond, overheating and dieing out. I guess you're running the catalyst drivers, with catalyst control center; if so, disable overdrive (overclocks ATI cards automatically, clock speeds are set in direct proportion to heat)
 
If overdrive isn't enabled, I'd be checking the card to make sure the fan is working, and also making sure the case had sufficient ventillation. (a good ventillation test is to remove the side cover, and see if the problem persists. [provided your gpu fan is working])

I haven't tried overclocking recently; overdrive is disabled, temperature is around 104-107F for GPU and video RAM as reported by ASUS SmartDoctor. Fans are running and side cover is removed right now.

Definately sounds like you've got crook video memory, or perhaps another related component on the card, if it's still under warrantee, take it back for a new one
 
If you want to convince yourself, maybe borrow a friends' card?

Yep I have seen that before. The card is fried and should be returned.
PS. return it with copies of those pictures and they should replace it.
S

Good idea steve, screenshots should help ;D