I found a generic 2 prong plug.
That's what the eBay listing was trying to sell folks, not the actual factory plug, haha. His add was a bit misleading based on the photos unless you read the entire description.
Sounds like as you said, the internal fuse to the 12 VDC output on the power supply may be blown if you get lights and the 120 VAC clock works. The Modulation light coming on when you key the mic and nothing else working gives me pause though.
There is a bridge rectification circuit on the at power supply board with 4 diodes that may have gone south not allowing 12VDC to reach the main board. There is usually a potentiometer on the power supply board that may need to be rotated a few times to get the DC voltage back up. If the filter capacitor on the power supply board has dried up (common) and shorted it may be preventing 12VDC output also.
If you have a 12VDC supply you could try and power the radio on the other pins of the power jack. The AC powered mechanical clock would not work, but maybe the radio would come back to life.