Wait did you try a different monitor- I can't tell from your post. If the problem does lie in your graphics card, then you either will need to get a different one (make sure you have enough wattage for the new one) or worst case scenario a new graphics card and motherboard. It's impossible to know exactly what the problem is without some more troubleshooting on your part but we can deduce a few components that should be running fine.
1. RAM (if this was not the case you would probably get a weird error message)
Another possibility could be the power supply. How old is this computer and is it under warranty? If it's under warranty, just send it back and save yourself the trouble.