Fullscreen artifacts (like the one you experienced) are symptomatic of GPU core failure. It means that the "CPU" of your graphics card is faulty. Artifacts like corrupted textures, Weird shadows in games, and other things that don't involve the screen/image itself is more likely to be memory-related.
It could also be the monitor. Can you try a different monitor? Or can you try to use a different video card on the same monitor?
Also, it could be that the card is loose in its slot. Make sure it is snugly plugged in the PCIe slot.