This happened with a Radeon 9800 Pro I had (because it overheated) and a Radeon X1600 Pro I bought later (due to a factory defect).
The lines and cubes appeared first in textures on my 3D games. Halo was covered in blocky multicolored corrupted texture maps, and sometimes things even turned transparent. In other games, and eventually even Windows itself, the mouse cursor's texture resolved incorrectly until you swapped desktop styles out and in again. It was a garble of pixels.
So yeah, I'm pretty much convinced your problem is with the videocard itself. If you use it in an overheated computer, or maybe the reseller you got it from left the box in the sun too long, it'll screw up exactly like what you're describing.
1. Try updating your videocard drivers. (lmao)
2. Send your card back to whoever you bought it from and demand a replacement. It's "defective."
3. Buy a new card altogether.
That's all assuming you're actually using a card that's not your default onboard, of course.
