How has a card that new failed already? Pull the heatsink off and re-apply paste, check to see that the vram chips aren't caked in dust n such. I found my primary HD5770 that I bought had an airbubble in the corner of the die in the thermal paste that wouldn't let it get over 1Ghz. (it capped out at 915-925)
I hope its not 100% dead.
My HD5770s are still running strong. The primary one when not Xfired has seen hours of gaming at 1Ghz core. When xfired they sit at 950Mhz each.
VRAM is running 1270Mhz (GDDR5) Samsung built (5G Modules)