Use something like MSI's Afterburner and see what clocks are set. Also, does it ramp up to 3D clocks under load? It sounds to me like the card (or the drivers) think it's idle, and the fans are spinning down.
Clear off any old (and the current) video drivers. Use something like CCleaner to be sure they're gone. Reboot, then install the latest drivers from AMD. Any change? If so, great; if not, RMA the card.
It's the card, I re-installed the drivers etc. tried a game (Borderlands 2) and it was the same with FPS issues, it eventually shut my PC down. The twin cooling fans were the fault. Returning it back to dabs.