I am running Debian 10 with an i7 4770K and two GTX 780TI. My monitors are on HDMI, DVI, and DVI. All 1080p60.
If I connect all my displays to my GPU then my PC will POST and go to GRUB like normal, but once I hit enter on GRUB I just get a blinking white cursor and nothing happens. If I connect my HDMI display to the integrated GPU via the motherboard ports (while leaving my DVI displays on the GPU) then I see POST, GRUB, and then the typical Linux command line boot text scroll past for 10-15 seconds then a black screen. At this point I have to unplug my HDMI monitor from my motherboard and plug it into my GPU and I will see the login screen where I can login and use the OS like normal. The only exception being that if I try to access another virtual terminal (ctrl-alt-F3, F4, etc.) I get a black screen. But if I unplug my HDMI monitor from the GPU and plug it into the motherboard then I see the virtual terminal and can use it.
I am genuinely confused by this and not sure what to do.