I don't know about the console world, but in the world of PC graphics, pixel artifacts and on-screen remnants are the first signs of GPU death.
I hope it's not the graphics chip dying or overheating, but if my PC was doing that, I'd assume that it might be needing a new graphics card, or a meatier power supply unit.
Good luck and fingers crossed it turns out to be something else.
 I don't suppose you can try it with the included composite cable thing, just to see if it still does it ??