Might try the following, in order:
Update the drivers. Probably not the issue, but better to be sure.
Check and clean the contacts on the vid card (external) where you plug in your monitor at. Typically, an air duster is enough.
If the cable is independent of the monitor (such as an HDMI cable), try using a different cable temporarily.
Check and clean the contacts on the cable (the old/original one, if you swapped as above).
If possible, try the monitor on a different PC (based on what you've said this should be fine and can be skipped, but never hurts to be sure).
--WARNING: the following steps might seem crazy but *should* narrow down the issue, assuming the above didn't fix it--
If possible, use a different power supply, if the vid card(s) is(are) powered (typical for PCIe cards). Further, check and clean as required the contacts. If PSU swap is not possible, and you have the tools, you could test the connections for the vid card.
If possible, try the vid card(s) in a different board. Further, check and clean as required the contacts on the card AND the card slot(s).
OK, enough of that. The first steps before the warning should eliminate the monitor(s) and cable(s) as an issue. Honestly, I hope its just a dirty cable - annoying but easy to fix.
The power supply going out could (but not necessarily) cause the problem you've listed.
Lastly, if you do everything, and the problem is still there (assuming the vid card(s) work fine in a different PC board) you may have a dying motherboard. Or at least the card slot is going.
The Czar