Thanks for the quick responses. I misspoke about my power connector. It's actually an eight pin outlet and I have 8 to 6 pin extension on it to attach to the 5770, but I suspect this is common knowledge amongst the experience. Unfortunately, my little town's computer store has no such Y-connector, so I will have to order one.
In the meantime, am I correct in my understanding that the six pin connectors run the fans only or do they supply voltage to the card itself? If they only run the fans, would it be feasible to run a single fan for a day or two? I have an Antec 300 case with all ancillary fans installed, ample room, and if the probe I have dangling in the center of the case can be trusted, temps inside the case run 28-30 degrees C.