On my other computer I'm using an old Powercolor AGP 2600XT. Rest of computer is Pentium 4 with 2 GB RAM. Whenever I try to run Team Fortress 2, Left 4 Dead, or some other game on it. It seems to run perfectly fine for a minute or two before producing no video.
The computer should be able to handle these games, and I have not really tried any other game.