I purchased the ASUS HD7750 silent, yesterday, I installed it in the ASUS P9X79 Deluxe motherboard running Win7 64, and first thing I noticed after powering up the system was some weird characters in the BIOS sequence, the HD letters had garbage characters etc... When Windows booted up, it installed its default VGA drivers and the HD7750 worked fine with them. I then installed the drivers from the ASUS CD that came with the card, after rebooting the system just prior to starting up Windows, the screen were filled by white horizontal lines and some pinkish squares, after few seconds the screen went blank.
I tried the latest drivers from ASUS site and even latest catalyst direct from AMD, with the same exact results!
I would tend to agree it sounds like you got a dud. So if you're still within the return period of the retailer you bought it from, you can request a replacement from them. If you're past that period, or maybe it was an open box unit so they don't have any stock to give you a replacement from, then if you're in the North America region I should be able to help you out.