Do you have that DC jack screwed into the chassis? Does the monitor have a ground pin?
Yes - both the switch and DC jack are screwed onto the small case - but the case is NOT grounded.
Yes, it is - it's metal, it connects to ground on the motherboard via the mounting screws, and ground on the DC jack via.. well, the body of the jack. It is grounded, and it totally, completely, and utterly bypasses your switch. This is in regard to system ground, not mains earth - that's another matter and may or may not be the same.
I've never had a computer case (outside of server racks) that were.
Every single metal case you've ever owned with an AT or ATX PSU is grounded. By the mounting screws.
Only two wires are on the output of that PSU so I doubt ground is provided on the output?
In this context the negative wire
is ground. Don't confuse it with the supply earthing conductor, which it may or may not be connected to (in the case of AT and ATX PSUs, many if not all monitors, some laptop supplies, ... and all sorts of other things, this is the case: system ground and supply earth are connected together).