^^^ This. Sounds a lot more likely that your black screen issues were early signs of a faulty, doomed card. Games don't hurt healthy cards. Its not common but sometimes they die—that's why they have warranties.
Most warranties are 2-3 years, and the 7700 series is not particularly old. Check, of course, but I think chances are good you can get an RMA. What brand is the card?
As for what other video card to recommend, that depends on your budget, power supply and what resolution/quality/framerate you expect. But a functional video card should not cause you any grief.