To test my above theory, do a leakage test from your DC power ground to earth ground. With the monitor completely disconnected, grab a large 10k resistor and jump DC power ground to earth ground. Measure the voltage across the resistor. Should not exceed ~25V (represents 2.5mA leakage). Anything over 5V (500uA) could be cause for concern. If that passes, then try again with a 1.5k to be sure. Should not exceed 3-4V. Measure AC and DC volts, though AC is of most interest. Also measure the individual rails to earth ground, but should not be different other than the expected DC offset from power ground.
Another way to check this is to use a low rated fuse (25mA or thereabouts) in place of the resistor (no meter then needed). If the fuse blows, then you have a problem.
This test can also be performed on the monitor isolated from the game electronics. This verifies the integrity of the iso xfmr (also useful on monitors with SMPS). Ken Layton earlier identified it as another suspect component for similar reasons.
You can also just try measuring DC power common to earth ground, but that can give misleading results.
If this test fails, then you have a faulty DC power supply which is shorted in some way. In a linear supply, there is a short from primary to secondary. In a SMPS, this usually would indicate a short in the transformer, but could also be a failed Y1 cap, shorted feedback optocoupler (very unlikely), or PCB flaw. Could also be any other component that is connected to both DC and AC line, of course.
Other useful tests are to check the iso as Ken Layton mentioned (should read very high impedance from either primary to either secondary terminal) as well as the same check on the DC power supply transformer.
It is possible that the DC supply transformer (if this is a linear supply) is an autotransformer (primary and secondary are not isolated). In this case, it was probably designed to run off the iso output. When you removed it, that would cause exactly this problem.