barakandl sells a wiring harness for $13 shipped. If yours is original I would recommend replacing it as it is most likely your issue.

Take a close look at the wires on the coin drop switches. Mine are constantly breaking loose.

Did you plug the sound board harness back in correctly? Meteor won't boot if the connectors are in the wrong places.

If you can't find a replacement try and find someone who does board repair. Coin op cauldren or some pinsiders do board work. If you have an electronics wholesaler or small appliance/radio/stereo repair company locally that may be a good way to go also. Redoing that 36 pin connector without the proper equipment and know how will be a rough go if trying to do it on your own. Like Chalkey pointed out replacing the caps would be a good starting point since its seems once the boards get hot is when the trouble starts. Redoing the capacitors by yourself is very easy and may be a good starting point.