Oh boy, where to start. First, I know you don't want to hear this but you can not rule out the connections in the head. You removed the glass and lifted the pf, thus pulling on the wire harness which is connected to your boards. From the sound of your beginning process I would suggest first replacing all of your connectors. Once you do that there are a few easy to complete grounding mods that will help your system 80. These Gottlieb Pins are notorious for these problems and I would have to look but I am sure you want to take care of your slam switch with a mod as that damn thing can cause much grief. Others will chime in but I would definitely start with the system 80 upgrades. GL and keep us posted with progress and further questions.

What coils are you referring to here? Pop bumper and sling shot coils?

First question, initially when the pin "would not boot" what would happen when you turned the power on? You messed with connections and stuff and it booted no problem, what would the Pin do when you turned the power on? Now you changed two (2) coils and some bulbs and it won't boot, what does it do when you turn the power on? Just making sure I understand and gather the information properly. Let us know.

Maybe the problem is with the voltage coming from the power supply board. Have you disconnected the cpu and checked the voltages at the power supply board. That rheostat for the 5v is worth checking out. Hook your meter up to test voltage then power down and connect cpu to see if you have a voltage drop.

wait, so the coils are locking on again too? If so you have a problem on your driver board. (The fuses are good right?) just checkin'.

I was just lookin at some pics and noticed that Pin has four pop bumper boards mounted on the underside of the pf, have you checked those out too?

Well, if you want to do the least amount of repining I would start with the ones that leave the driver board and go to the pf. Did you add the extra wires on the jumper harness too between the cpu and driver board? Also, re-tinning is good but you have to be careful and there are many in the board repair industry who don't really agree with this practice, just some food for thought.
As for the pop boards if the original problem came back those boards have transistors and other components that can go bad thus locking a coil and/or sending voltage back to the driver board or cpu that should not be there. I had one of those boards that failed and it burnt the coil and the two driving transistors on the driver board.

Glad I could jog your mind!