When you say in "certain games" that implies not every game gets this black screen problem. That would suggest that it's related to the game (or some other software) rather than the hardware. So,
What is the refresh rate set to in Windows itself? Because even when I hooked up my 144Hz monitor it stayed at 60. I had to manually change that. It's under display settings - advanced display settings. Try this first if you haven't already.
What game(s) have this problem?
Do you know what resolutions the games are set to run at?
I'd try changing the games resolution to something really basic and see if it'll display then. Ditto more advanced display features. You could either use your old card and change the settings then swap to your new card. Or most games will let you change settings using notepad to edit a config file if you don't feel like repeatedly swapping your video cards around. Just be careful doing that because you can screw up the game settings badly and need to reinstall the game.
Once (if) you get it displaying again then tweak the display settings back to something better.
Oh, and if they're already on low settings (like 720p), it might be worth bumping the resolution up. Try setting the game to the monitors native resolution.
