Your PSU is listed as providing 20A per 12V Rail.
I've got a 700W PSU that only has 2x 12V plugs but each pushes 25A. I've never tried to run multiple cards on it though. I'm unable to find specific amp requirements on either card but most PSUs with 4+ 12V rails seem to only offer 20A per or less. I found a Zalman 850W that sports 25A per 12V but it costs over $250...
I'd be inclined to say you've got enough amperage unless the PSU is on its way out. What version of the ATI drivers are you running? I'm not convinced drivers are at fault here but now I'm even more curious

This is probably totally unrelated but how much RAM does your PC have?