I have a GTX 560ti that black screens when launching a game. I can run it all day long in Windows and it'll be fine, but once I launch a game it crashes out to a black screen. I have to do a hard shutdown to recover.I  previously had a GT 640 which worked fine, but the 560 is giving me nothing but hell. I tried the steps from another post about the HD Audio Driver issue but it didn't make any change. I have the latest drivers directly from Nvidia site. I only have the graphics and PhysX drivers loaded. My system details are listed below:
 
HP Pavillion a6750f
Kentec 750W PSU (upgraded from stock)
AMD Phenom X4 CPU
8 GB DDR 2 RAM
Win 7 Ultimate

I downloaded the Afterburner software as you suggested. I increased the fan speed and also downclocked the core and memory speeds. Even after this the problem still persists. I tried my card in my friends computer who also happens to have a GTX 560ti and it worked flawlessly. I really think the problem may now be the PSU so I'm looking at replacing it. This time I will go with  your suggestion and get a higher quality. My friend has a Corsair in his so I may go with that brand. Thanks for all the suggestions and help. I'll update this post after changing the PSU and let you know if that resolved the issue.