This was among the first things tested, including BIOS reset. Sorry for not mentioning it, I just take it for granted that stuff like this is tested first.
The board has no onboard video at all, so there is only autodetect, pci graphics and pci-e graphics, which was set.
But like I mentioned above, it started out of nowhere, no settings changed or HW added before it started happening. Also, both DVI connectors exhibit the same problem.
It's irritating. Having another PSU for test would help, but nobody near to borrow one from.