I think the problem is this >>
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Just kidding bud!
What power supply are you using? Are you sure it's strong enough for the 7970, if you are unsure, can you verify this on another system possibly with that card and PSU? Also, can you verify on another system that the 7970 itself works at all, just to be sure it's not DOA
Are you using the latest BIOS for the board? If not, please update to the latest as this may correct the issue. If the latest BIOS listed on Gigabyte's site does not help, try the latest beta as it could contain a fix for the issue, you can get that BIOS here
http://forums.tweaktown.com/gigabyte/28441-gigabyte-latest-beta-bios.htmlAlso, have you tried booting with the 7970 in the other PCIE slot (x8)? If not try it and see if that will allow it to boot.