Hi, The next step would be testing a different graphics card and see if still the sme. Can you borrow one? This way you'll know if it's a board-CPU issue or a GPU one.
I tried what you told me and surprisingly the rating of my Sapphire 7770 Vapor-X is 7.6 on both index, it seems to me that my power supply can't power my 7870?
This was my old rig
8gb kingston DDR3 ram
cougar CMX 700w
Sapphire 7870 OC
when I bought the second one I was going to exchange the 7770 and the 7870
Sapphire 7770 Vapor-X
Corsair Dominator Platinum 1866 2x4gb
Seasonic X760 760W
Seagate Barracuda 500gb 7200rpm
MSI Z77 Mpower Bigbang
23' 1080p Samsung
So still i dont understand why the current rig is having problem with the 7870