I'm not a computer expert by any means. I tend to tinker from time to time myself but for what it's worth:
Your idea would lead me to believe the same thing: its your video card. Another possibility that it might be is that your power supply is also full of dust etc and burned itself out. Have you received any power spikes/power bumps lately? It'll have to be replaced then. This happened to me and even with a "surge protector" I actually fried my motherboard. The computer still works but not to it's proper function(s) and sometimes intermittedly. You can tell this by looking at your MB. If the capacitors (if you don't know; they look like little pop canson the board) have "popped" it's fried. The tops are supposed to be flat, not curved or even have stuff 'leaking' out of them.
Last but not least it might just be a virus. If you actually get it running on the net do a search for "Housecall". Its a free online virus scanner. It'll ask you to download something but it's required to do the search then let'er fly. I've saved a few PCs with this.
Pending that, you're into a bit of money. If that's the case upgrade to a MAC
!
Just a few ideas.....
Just a newbie.........