Bally’s of this era are known for connector issues. Basically, you should repin all connectors, male and female.

Great Plains Electronics is a good source for pins and connectors.

Do a search on Pinside or Utube on crimping pins and replacing connectors on Bally circuit boards.

Just replacing all the boards with new ones will not take care of the problem - you will need to replace the pins in the connectors. Unless you send out the wiring harness, you will have to learn how to do this. It’s not hard if you have the right equipment - just tedious.

For every Bally I have owned, I have rebuilt the power supply and re-pinned the connectors and plugs on at least the Solenoid Driver board and the MPU. The life of these pins is basically 25 times unplugged. I usually only do the light driver board if there are apparent problems. Do these things and they are basically bullet proof.

With Bally SS games you need to learn how to solder.
95% are bad solder joints at the print headers on the boards.
Like you say about the displays.
Reflow the solder on the print header and they will most likely be fine.
The lamp driver and solenoid boards have the same kind of problems.
The power supply needs to be rebuild if you want a good solid power supply.

1. Learn to solder.
2. Buy the proper tools: wire cutter, stripper, and Molex pin crimper. May also want to buy or make a tool to remove the old pins from the connector housing. You can reuse the old housings if they are not burned out or broken, although new ones are not that expensive and easier to just replace with new.

As others have said, it is tedious, but repining and reflowing old solder joints will fix 99% of your problems in the old SS games.

Review this topic for tips and tricks on soldering:

https://pinside.com/pinball/forum/topic/terrybs-soldering-guide-part-1

reflowing the pins on the displays is often good enough to get them solid.

As you have limited solder skills I would probably only address the things that are having issues. I would find some old dead board to practice on.

As others have said, don't mess with the molex connectors on the displays. They are almost never bad! Just reflow the solder pads on the displays on the back side of where the molex connector plugs in. If you look at the solder pads with a good light, you will likely see rings around several of the pins where the solder pad has broken. Usually at one end or the other. Two seconds with a solder iron and a bit of fresh solder and you will be as good as new for another 25 years!