I had to put all PCI-e slots into x1 mode in BIOS on one of my P67 rigs. Otherwise it would say the video BIOS wasn't invoked. After that 4 cards worked.
i can't find/don't have that option in bios

here is link for manual:
http://download.gigabyte.eu/FileList/Manual/motherboard_manual_ga-ex58-extreme_e.pdfI have found confirmations that with BIOS version F13J 58xx and 69xx series cards definitely work. You could try that.
Also, I would try re-flashing your video card's bios as well, in case your other test computer is just a little more forgiving of some minor problem in it.
i do have BIOS F13Q. link on how and where to get new bios for video card?