You can start here in the troubleshooting part of the manual on page 14. . .
https://www.ipdb.org/files/1823/Bally_1978_Playboy_Manual.pdf

For me, I'd start with the power supply and rectifier board. Make sure you're getting the correct voltages from all the test points on the board. Be careful when taking readings as there are lethal voltages on that board. . .

The rectifier board and the pins and wires going to it are usually what go first on old SS Ballys. The rectifier board is what turns AC current into DC. The bridge rectifiers on these boards and the connectors to them tend to go after so many years. Also - the fuse holders sometimes just have bad connections and need to be cleaned or replaced . I've been working on a 1978 Bally Mata Hari and this was one of the big issues that I had to fix first -I replaced it for $60.

https://www.pinballlife.com/mm5/merchant.mvc?Screen=PROD&Product_Code=PBL-100-0070-00

Replacing a rectifier board does involve some desoldering and re-soldering 10 or 15 wires from the transformer to the new board so you'll need to have that gear. I was able to find a kit with the board and new pin connectors.

Next I would check the MPU. When you turn the machine on there is a little green LED at the bottom center of the MPU board. It should flash 7 times when it boots. If it flashes less than 7 you probably need a new MPU board. Check when its cold and warm. Things always go screwy when they get warm.
The MPUs often have problems from the old batteries leaking on the bottom of board and damaging the board. Also the connectors and pins can go bad. One cheap option is you can pull the board and reflow all the pins and then pull the chips clean the contact on all the chips with a fiberglass brush. Mine had intermittent problems with the display until I figured out which chips and traces were bad. Intermittent problems mean intermittent connections. You can try to find them and fix them but replacing the MPU board is your best best with all the problems you are having. $200 for a new board.

https://allteksystems.com/collections/pinball-replacement-board-products/products/ultimate-mpu-universal-bally-stern-replacement-board

The next issue with older Ballys are the solenoid driver/voltage regulator AS 2518-22 boards failing. The solenoid board is what fires all the coils and supplies higher voltage to the flippers and score displays. It sounds like yours is sort of working if it is able to trigger all the coils in the test mode. You can check the voltages on it as well to be sure it's working.

There's some bullet-proofing improvements you can do to the back of the board.

The capacitors often go bad on them as well. When coils don't fire or get stuck on it's bad transistors on the solenoid board. This board has a high voltage section of 230V DC so be careful and unplug before working on it. The capacitors also can store some of that high voltage so be careful around the big caps even if the machine is turned off.

The good news is you can get refurbished or new versions of the MPU and Solenoid boards for around $334. Alltek makes new ones and a few other companies.

https://allteksystems.com/products/ultimate-mpu-w-solenoid-driver-board-bundle?pr_prod_strat=description&pr_rec_id=860d1edfe&pr_rec_pid=3882420142125&pr_ref_pid=3882420994093&pr_seq=uniform

If you want to save money you could also put up a wanted ad here and there's people that have refurbished boards for less than the cost of the new ones . . . Good luck!

If you swap the MPU and it still has intermittent problems it’s definitely the connectors. After 40+ years you either have cold solder joints on the pins of the old MPU or bad trifurcon connectors in the headers. It sounds like you have the proper tools to redo the headers. However, if you don’t, I ordered one of each of these tools which made quick work of the repair.

HT-225D Full Cycle Ratchet... https://www.amazon.com/dp/B007JLN93S

Hakko-CHP-170 Micro Cutter - Red https://www.amazon.com/dp/B00FZPDG1K

Capri Tools 20011 Automatic Wire... https://www.amazon.com/dp/B01018CX46

The old boards are reliable if they haven't been too damaged by the battery leaking. The MPU on the Mata Hari i'm working on had corrosion on all the chips and resistors near where the battery leaked - there's is acid inside of those batteries! Some of the traces were even damaged and jumpers had to be soldered in to fix it. . .

If your MPU seems clean - the connectors usually are the culprit of intermittent problems. If you can try pulling the chips that are in sockets and cleaning the contacts.

Let us know how it all works out.

I think the early SS Ballys are in a sweet spot right now where you pick one up with these type of problems for under 2K.