I would suggest that it is a hardware issue. To check, it might be a good idea to switch the monitors over and see if the problem is still on the same monitor or if it has moved to the other one. You should also try just swapping the cables to see if that's the problem.

If the problem sticks with the same monitor even when connected to a different output and changing the cable makes no difference then I would say there is something wrong with the monitor. Otherwise I would say it was the graphics card. But make sure you test the cable.

I get this same problem myself with a snowy effect and flickering if my cable comes slightly loose at the back. It may be something as simple as a bent pin in the cable head which isn't quite connecting properly and can be bent back (had that problem in the past too).

The software crashing is probably due to the PC thinking you've disconnected the monitor and just not handling that very well.