After putting together the machine and on first post the machine lit up and fans operated however no display. I checked the graphics card was seated properly and tried again, no joy, also no warining beeps at all.
Removed graphics card and tried (Mobo has onboard graphics) and machine booted fine. I then went into BIOS and disabled the onboard graphics and set the display device priority to PEG. Refitted the graphics card and same result nothing!
I then removed an HIS 5770 card from another machine, fitted it and it works fine no problem. Thinking at this stage the the XFX Radeon HD6850 was DOA I then tried it in the donor machine and it works fine!
From the trawling of the net I have done and reading into the specifications fully this card should work with this setup. The board has a PCIe X16 revision 2 slot and the card is revision 2.1 but from my research this shouldnt be a problem and it wasn't for the 5770 I tested it with?
Is this a lost cause and do I need to look at an alternative card (any suggestions would be good as can't find any compatability lists) or have I missed something?
I have the exact same problem but with a VTX HD5870 and had already tried pretty much the same things as you. I have tried all BIOS updates for my Rev1.0 version of the Gigibyte Mobo. I too have the hex core AMD cpu and similar HDD and RAM spec on the same mobo.
Many months ago I did manage to get the PEG graphics card to work for a while using PEG display first in Bios and disable onboard graphics but the system would reset randomly after a month or so and even more strange was that only a CMOS reset would restore the system to a working order using the onboard gfx.
In the end I just gave up using the HD5870 and have mothballed it until I get a new (non Gigabyte) motherboard and RAM upgrade to see if that works.
SOrry I can't help but at least you know you are not alone.