I would suspect a loose connection of some sort, probably with the other two cables. It could also be a different HDMI standard being used on the monitor that isn't supported by the older cables.
In order to test the switch, get your multimeter out and set to ohms or continuity. Your going to test across the switch with nothing activating it FIRST, then ACTIVATED. All you need to see is the switch change states then you will both know if it's NO/NC and if the switch works. NO = OL to Ohms (or beep) NC = ohms (or beep) to OL
Something is giving the computer a shutdown command. Either a stuck button (maybe the power button getting stuck pressed), hotkey on the key board pressed, or a program that requires an update.
