#1 : NVidia driver. You DO need a fairly recent version to run with a 780Ti.... Go download and install the most recent WHQL version: (once you go back to your GTX580's re-load the drivers Again....)
http://www.geforce.com/drivers
#2 : I've read a ton more post on "issues with GTX 780 & 780Ti's not booting or going to a "B2" error screen...."
- one of the fixes
IS to update the motherboard BIOS.... (hey, I learn something New everyday....)
SO, Flash to F6 and post back .....
Then, Flash to U1L and see if things are still working with the GTX 780..... (no worries there, you can always just flash back to F6 Again if you run into trouble...)