Did you uninstall the drivers for your old card completely or just put the new one in and install that? It might be worth removing all of the software and deleting any drivers for you old card and your new card. Then installing your new card again.
If you havn't already go to the manufacturers website and download the newest drivers. click here
Does this only happen when you go into games? Can you ever get further than the game menu?
You can also check if it's a Direct X problem by going Start --> Run and typing 'dxdiag', then go through the tabs, check that the window at the bottom states everything is ok, and you can run various tests.
I have a Sapphire Radeon X800, and found that if Anti-Aliasing is enabled, or if it's set too high then the game crashes. For one of the games it does it on, Call of Cthulhu, it's a problem with the game not being compatible.