OK, so the monitor is connected to the isolation transformer.
There should be two wires coming "out" (which run to the monitor) and two wires going "in".
If I understand you correctly, the "in" wires were connected to the arcade power supply and are now disconnected.
If that is the case, what you need to understand is that those wires where not connected to the "output" of the PS (the PS puts out +5VDC, +12VDC, -5VDC, but no AC), but rather just tapped off on the input (which is AC coming from the wall and IN to the PS). While you don't need the PS anymore, you still need to provide AC power to anything that was connected to the AC poles on the PS.