Quoted from EMsInKC:

Chimes are a function of the individual point relays. The 10, 100 and 1000 point relays all have switches that power the chimes. But since they are working them stop, I suspect you have another common chime issue.
Usually they used beer seal on the bottom of the chime unit for the plungers to drop onto, so you don't get a clunk when the plungers return to rest. Those plungers warm up during play, and they can easily pick up gunk from the beer seal and the plunger ends up either stuck on the beer seal or stuck in the coil sleeve. You'll need to take the chime unit apart to see what is going on there, but since it works for a few games and then stops, I suspect that as the plungers heat up, they're sticking.
As for your credit unit, you're saying that it will not step up for coins being deposited, high score replays, special replays, or matches? If so, the first place to look is your max credit switch on the unit itself. There is a peg on the gear of the credit unit that will open a switch at 0 to not allow the start button to work, and also a separate peg on the gear that opens at switch, normally at 15, to keep more credits from being added to the credit unit. If the max credit switch is open you'll never be able to add credits to the game.
Is the credit reel at 0 or totally blank. Gottlieb games do not go blank (Williams games do) but should have a 0 showing with no credits left. If you're truly at blank, your reel is out of alignment. You need to get it set so it is at 0, and the 0 position switch is open, max credit switch closed. Then if you want to have free play, either jumper the 0 position switch closed, or just bend the switch permanently closed.
Is the ball in play unit stepping up properly? The unit is in the head and at reset the shoe will be off the rivets. Each time the ball crosses the trough switch it should step once. On ball five, when the outhole is made, it will step to the sixth rivet position and open a switch which kills power to the playfield and ends the game. I suspect your ball count unit is out of adjustment.
Let us know on any progress.

Quoted from EMsInKC:

I think you misunderstood. The steppers have to work properly. There's no ifs or buts about that. If they don't, the game is never going to function properly.
I'm not advocating tearing them completely apart, but you're going to have to do some work on them if you want your game to work. There's just no way around it. There's a lot of games out there that don't work because the steppers have hardened up grease in the gear, or the rivets are all gunked up and won't function properly.
Will the game play, to a point, if you don't get them working fully? Yes. Will it function 100 percent if they don't? No.
The main problem I've seen from beginners on here is that they start out with games that are more complex, meaning, multiplayers. There's just more to a multiplayer than a single player game. And because they made a ton of them, a lot of them start off with a Grand Prix, which can be a daunting game even for someone with experience. There's a lot of them still around and as such they're more available, and people buy them not understanding exactly what they're getting into.
I understand your idea to fix one problem at a time and it's not bad advice, but there's times when problems are interrelated and it's pretty hard to do.