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5770/6770
They require 6 pin power connectors hurp durp
I think it is the cheap PSU that should be careful of. Sounds to me your PSU wasn't providing stable enough power to the motherboard/PCI-E slot...Be careful of cards without external connectors. I had a cheap PSU and motherboard where it was fine with a HD4850 (1 6 pin power connector) but refused to boot citing a power issue with a 4670 (no power connectors).
I think it is the cheap PSU that should be careful of. Sounds to me your PSU wasn't providing stable enough power to the motherboard/PCI-E slot...