If it worked with the 780 before, I would not assume the MB BIOS does not support the 980 RCoon. Like I said, I have seen this before with 970s on MBs as old as the X58 series, and a BIOS update fixed it.
That said, what's going on now appears to be either WBM, OS or BIOS corruption, since it won't even boot up with the 780. In that case if Safe Mode is not operable to try and initiate a repair, I would format.
It may be possible however to do a CMOS reset Paul, which sets the MB BIOS back to the factory safe settings. Any MB manual will explain how to do this. On the more modern MBs, it can often be done with the push of a button on the MB.
On older MBs like X58, you may have to use the jumper method, which is how it's done on my X58 ASUS. The jumper method is basically 3 pins on the MB, with a plastic cased metal cap (jumper) that creates a connetion between two of them.
The manual will show where the CMOS jumper is, and explain what pins to put it on to short the battery connection, which is what resets the CMOS by wiping the BIOS settings memory so it can default to factory settings. You let it sit that way several seconds, then put it back in the position it was in, pretty simple.
The hard part is actually reaching it and being able to see well enough. Setting the case on it's right side under bright lighting and using a pair of tweezers is the way yo go, with power unplugged of course.
If this all seems too daunting, you may want to have a shop try to reset the CMOS, and if that doesn't work, format it for you.
[Edited}
Just read the bit about having already arranged help, but I thought I'd add something for future reference. In case you're unaware, it's possible to cause system corruption just via simple things like getting impatient and trying to reboot or shut down in the middle of reboot/shutdown process.
Hopefully you'll get it up and running soon so you can shred some games on that new card.
