Naruzeldamaster
Auror
A few of the more recent games I've played have like an 'uncapped' mode for frame rate and it's (stupidly) always on by default. Which really really pushes my PC.The best way to know for sure if to find something that is known to be good and test with that. If you move the monitors to a different computer, does the problem move with them?
Of, if you put a monitor that works on one PC, on the failing one, does the problem go away?
Something hardware sounds like the problem. It would be unusual for both monitors to go at once. It would also be unusual for a Vid card to go bad and not hose the whole machine.
Moving monitors around is the easiest thing to do, just need another working PC.
Video cards can be set to things the monitors dont understand (like 300 FPS, when the monitor can only do 120), but that is unlikely as it would mean someone manually changing it, which I doubt you would have done.
Turning that setting off and setting the game to 60 FPS lock seems to fix it every time. My PC might be a gaming PC but it's not 'designed' to run games like that. Plus our eyes stop seeing improvements at 120 FPS (I think ) anyway.
I don't know any video card that sets to display frames at a rate the monitor itself can't handle though, at least not by default.

Scribe