I definitely waited enough to see if it would finally load expecting the black screen initial with the non efi card.
Well, I just experienced the same constant "black screen" issue on a GTX 680 that had been working previously (unflashed) on a MacPro5,1. Let it sit a LONG time (it's usually a 15-20 second boot, MAX). Nothing. Reset PRAM. Nothing. Wasn't getting volume controls after chime/boot either. The drives would show up on the network from other Macs, but could not access screen sharing and the system would simply not login.
Left with no other way to troubleshoot, I resorted back to the original configuration and swapped in a stock 5770. There were no issues booting, system showed desktop perfectly fine. Volume controls worked, all drives were accessible, etc. The only sign of a problem was a random date/time error. Appears that the "watch" battery on the motherboard might be dead (or dying). I'll swap that out later today.
It's worth checking out the battery or replacing it. It's located behind the graphics card slot, so you'll need to remove the graphics card to swap out. Stock battery says BR2032 on it.
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Update: Just replaced the battery with a CR2032 and added the GTX 680 back to the machine and it's working fine, just as it had been previously. The package for the "2032" from Energizer says replaces all size 2032 batteries.
Update #2: After a system restart, the screen is once again black and not booting into OSX with the GTX 680 installed. Not entirely sure what's going on. Card is fairly new on this machine and was working perfectly fine for over a week. Attempting to troubleshoot.
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Final Update: This GTX 680 card is being returned. After one solid week of use, this issue appeared and no reliable remedy after a few hours of troubleshooting. The "random" solid black screens after full boot aren't worth the cost savings and I will be getting the EFI version. First time I've ran into this type of an issue with a GTX 680, and it figures it's on my own machine this time (and not a client's). I need reliability, and hopefully the "Mac Version" of this card will provide more of that. Was finally in-stock again, so went for it...
The non-flashed GTX 680 will boot fine the first time immediately after it is swapped with the 5770 (installed, booted, used briefly and then shut down). But the GTX 680 will not boot after it has been shutdown. Tried removing all cards, removed all but main system SSD, and all resets. It wasn't the power cables - both independently powered the 5770 without a problem (only one 6-pin required).
Will not be getting rid of this stock 5770. Reliable backup that works and good to have around, if needed.