What voltages are you reading at the other test points on the rectifier board? I wouldn't be worrying too much about TP2 right now, you need to be getting 12 to 14 volts DC at TP3 first for the logic boards to operate.

You now need to measure the voltages on the solenoid driver board test points.

You need to find out where the bad connection on the 12 volt supply from the rectifier board to the solenoid driver board is, i.e. you're measuring 12.5 volts at TP3 on the rectifier board but nothing on TP5 on the solenoid driver board.
The 12 volt supply wire is from the rectifier board J3 pin 8 to solenoid driver board J3 pin 12. Usually it's an orange wire.

Note, now that you have the solenoid driver board hooked up, your high voltage for the displays is measuring correct on your meter although you should adjust the pot on the solenoid driver board to get TP2 measuring between 175 to 190 volts but leave that to later. Deal with the 12 volt issue first.

Unless the old connector housing is badly burnt, just re-use it. Slightly brown, don't worry about it.

Are your displays working? If yes, ignore the TP2 reading, it's an anomaly due to the 100k resistor at R3 on the rectifier board and the input resistance of your multimeter. If you want the proper voltage reading you need to measure the other side of the 100k resistor.