First make sure you have all the most recent ATI catalyst driver, as well as DirectX drivers. I run a 5850 and the only game I had trouble with was Bioshock in Windows 7 at first, but after I updated everything it worked fine. So streamline your system and make sure the games you are running have the most recent patches for your OS.
If it happens to be your video card is malfunctioning,contact ASUS for support. Good Luck.