Here is my problem, am building a mid-range gaming computer for my nephew.
when the ATI 5770 is installed in the PCI-E X 16 slot (with the 6pin power connnected) the system turns on and off every 3 seconds, They told me that I needed a better PSU, so I installed OCZ MODX STREAM-PRO 600W, I have the same problem.
When I stick the card in the PCIe X 4 slot, it WORKS.
You can try to update your bios also, that usually fixes problems. I do not know if it will fix yours, but it's a try.
Some 5770 that are PCE-E 2.1 have bugs on an older slots like PCI-E 16x. So the update might fix your issue. Also i recommend as well to test another card on that system. And try the 5770 in another system as well, if it works there, the cad is fine.