Yeah, The Jennifer is right, what an ugly hack-job.
Looks like they took the Sente power board (the thing with the black heat-sink) to route power to the Jamma loom, while using a modern power supply (grey) for what looks like a PC's Mini-ITX power supply for the monitor. It probably has a small transformer inside that block, but I wouldn't really know.
Can you confirm the grey power supply connected to the Monitor?
They completely bypassed the original monitor transformer by the looks of it. I bet it's still good. From this hack-job, I don't think a simple swap-out of the power supply is going to cut it.
Personally I'd pull the original PS (board with the black heatsink) out, and re-wire the cabinet's power from scratch, using the original transformer.
Get rid of that crappy grey PS, I'm willing to bet that it's dead from trying to power that monitor...
AC wiring is very simple, Bob Roberts has a very straightforward guide to wiring it up from scratch:
http://therealbobroberts.net/acwiring.htmlGet yourself a switching Power Supply, as pictured in this guide, and have that run to the JAMMA loom.
Your picture of the Tetris board confirms that it's a JAMMA board.
For a JAMMA Tetris
board's pinout you'll definitely need +5v, +12v, and -5v for it's operation.
Follow the JAMMA wires and connect the appropriate wires to the pins of the loom.
Also, get that board off the metal! Mount it on some wood using PCB mounting feet!