I recently got an Visiontek Radeon 5850. On installation with the one 6-pin PCIe adapter inclulded, I got no post, no video, and an infinite beep from the card. Posting this question so I can answer it in hopes that someone else finds it useful.
It simply wasn't getting enough power. I purchased another Dual Molly 4 pin to 6 pin adapter and jumped out a second PSU. I now have one PSU running the computer and another running the card. And it works, runs fairly stable.
When I say runs well, I mean Crysis 2 with all settings on extreme and the card is a little overclocked.