Hmm...That still sounds like the exact same issue I was having. (Since it's new I'm fairly confident in the assumption that you're running XP) Try this: Right click on My Computer and go down to properties. Click on the hardware tab, then on device manager. Expand the tab that says "display adapters" and make sure that it says "ATI x600" (or something to that effect).
You could also just check under properties on the desktop, and look at the display tab. If it's running it without utilizing the drivers properly it won't mention what kind of card it is.
I apologize for seeming so insistent, but I had the exact same problem when I first put XP on my machine, so I'm about 95% sure it's a driver issue.
Ah, that reminds me, has it been doing this since you got it? If not, did you install anything just prior to it's acting up?