No. I have yet to see an infection that actually gets into the firmware. So the video card is fine. We just need to get rid of it, it might be in the drivers, it might be someplace else. It is theoretically possible it is in the hardware, but as far as I know no one has proven that it exists in the wild (internet).
As for your suggestion being way off, don't worry. We all started in the exact same place. I made some fairly wild assumptions when I first started, but the folks that taught me had patience with me, I would be repaying them poorly if I did not have the same patience with you.