Past posts certainly show that this board has a litany of issues, though I haven't found this one in older posts:
I needed to put a different brand of Radeon HD 6570-based PCI-E card in the system so that I could use the existing card (a low-profile model) in an unrelated system that required it. I figured this wouldn't be an issue, since while the cards are different brands, they're functionally identical. Neither even uses a separate power cable, they're that low-end.
However, when I use the PowerColor AX6570 1GBK3-HEV2 instead of the SAPPHIRE HD 6570, the system doesn't boot. LED reading shows 15, which means that it stopped around LAN device initialization (I've seen people report this in the past with other scenarios). The LED strip never illuminates the 7th one, which is what it should if video is working. It gets as far as the 5th and 6th (processor and memory).
Even though it didn't make sense, I checked out the video-related BIOS settings (with the old card in), and the only thing to change was the one pertaining to the primary video adapter. It was on Auto, so I put it on the specific PCI-E item. Of course, that made no difference.
BIOS: 0028 (certainly not going higher with Sandy Bridge)
I would put the original video card back in the DZ68BC, and buy another low-profile card for your other system.
I are right about the risk with upgrading to BIOS. BIOS 0028 is the best for Sandy Bridge (based on my personal experience, and once upgraded there is no way back..). The release notes of BIOS 0039 also don't show any special fix for external video cards.
I guess it's just luck of the draw. Even the other slot didn't help, but the card isn't actually bad, since I tested it in an unrelated system. Oh well. Not that Intel is updating the BIOS for this board anymore, but it would have been nice if this Sandy Bridge/Ivy Bridge BIOS split never happened. I never really got to update it again after the initial flash a couple years ago.
FYI: There is a new BIOS version (fixes the "unsupported CPU screen at startup), but you need to contact Intel support for it as it is not published. BIOS 0028 is still better for Sandy Bridge.