A software problem seems more likely, though it sounds like you've had the problem as long as you've had the TAM. I assume at least one of those OS upgrades was a clean install.
The only hardware fault I can imagine causing that sort of problem is the built-in video tuner. It does display in that sort of constrained-to-a-window (though it's usually colour-keyed), and if it were flakey it might conceivably do something like what you're seeing. While messing around with different ATI and TV/video drivers on a TAM, I have managed to get video to pop up spontaneously in windows with the right colour background.
You've obviously not getting video (it wouldn't appear in a screenshot anyway), but something is trashing video RAM inside a particular window. You might be able to test this by disabling the Video Startup extension (plus all of the ATI extensions if you like). Alternately you could pull the tuner card out, but that's a reasonably expert operation.