Hey guys. Is there such thing the graphic card not compatible w the monitor?

I have an old benq g900hd 16:9 lcd monitor and i bought a new pc w a grapcic card gtx 960. I have to use certain resolution for my monitor to turn on and when i play games like cod, the game kind of stuck and one day my sister played diner dash the monitor crashed.

Help

run 3d mark u will know monitor crash or pc crash