This is going to sound a little weird but bear with me...
If you look at the back of your computer (unless you have the MB mounted upside down.) your adapter should be in the DVI Slot on the right, or the one that is further away from the MB, closer to the case door.
Never been there. I created this PC just a few days. I had a MSI P45 DDR2 Socket 775 with a Radeon HD4870 512MB.
Maybe try and put the 4870 back in the PC and remove the 6970 to see if EFI is still broken ?