Start with one problem and work through that first:

The score reels not turning - each score reel has what's called a 'carry over' switch - except for the last one. Observe the reels that won't turn the next, like the 10s through each step (from the back). Compare to the 100s which does advance the 1000s. 10s should look and operate the same as 1000s.

Then, move to the other problems. One bite at a time!

Take a look at the schematics, around section 21, you'll see the 100pt relay coil. Tracing the wire down (W-R) you'll see it's connected to the L and R Spinner Relays, as well as, farther down, the 1-4 player "10pt du 9th pos sw" via a switch on the 10pt relay (meaning that when the 10pt is energized and the 9th position switch is closed, the 100pt will also energize. (a coil energizes whenever there's an unbroken signal from the left hand side common wire, through any combination of switches, to the coil, and then through to the right hand side common wire) To narrow down the switches further, check whether the 100s reel also doesn't advance when 10s rolls over for players 2-4. If it's consistently not working across players, then, it's probably the switch on the 10pt relay, since that's common to all four, unlike the other switches on the 9th positions and in the player unit. Once you suspect a switch, use a jumper to 'bypass' the switch (or series of switches if it's a longer chain of them controlling a coil), and see if the coil fires properly, and adjust the switch if so.

Same goes for the other score reel and the ball count. Find the coil, trace the switches across, check and/or bypass each one till it works and you find the problem

I won't be very helpful for the tech part but all I can say is "Good choice, this game deserves to be restored !" .
Collin nailed it on his evaluation of this game (see ratings). A great Williams EM.
Realling considering adding this Williams to my lineup.

It's more than just the nine position switches. Each score reel relay, except the 100000s, has a switch that sends power to the next score reel relay up when the game goes from 9 to 0. You need to check that in addition to the nine position switches.

I have a Grand Prix and it would get stuck on ball two. There is a stepper unit in the cabinet for ball count. Make sure that is stepping smoothly and resets properly.

Www.pinrepair.com has an em repair guide with a section on steppers. Good place to start. I never got around to mine

Pinrepair.com is a great place to start. There are also a couple youtube videos if you have trouble visualizing. For the record I haven't watched these so I'm not sure how good they are.

I clean the surface with Alcohol, and then use 400 grit sandpaper to clean the surface. I scrub the contacts to a shine and clean the surface again with Alcohol. You'll have to manually move the coil unit so you can get to all the rivets, or better yet, remove the finger disc.

From Clay's guide: "On a Williams stepper, there is a 7/16" nut which holds the finger disc in place. To remove this nut, on the opposite side of the stepper, put a small screw driver into one of the large holes in the stepper cog to prevent it from turning."

Once off, I carefully shin the bottom "fingers" of the disc with 400 grit to make sure the contact is solid.

A lot of people apply a thin (very thin) layer of Super Lube to help the steppers move easily.

http://www.amazon.com/Super-Lube-21030-Synthetic-Grease/dp/B000XBH9HI/ref=sr_1_1

Follow Clay's guide (2D):
http://www.pinrepair.com/em/index2.htm#top

Great job! Keep it up and you'll have it 100% in no time.

Did you make sure all the wiper blades are making contact with stepper unit? You could also check that there isn't some "play" in the unit and the blades can be pulled away from the surface when it rotates.
You could also try cleaning the blades' contacts with some sandpaper.

For any problem, I will look for a coil that I think will be involved with the problem. In this case, a likely suspect would be the ball count unit. I am not looking at a Grand Prix schematic right now, but I believe that you would like to examine the switches in the circuit for the Ball Count Step Up Coil. Follow the ladder backwards, checking each switch along the way.

Hi Madpole +
You are doing great - a pleasure to read this topic.

About "Not advancing to next ball": Can You start a TWO-player-game ? And - at the end of Player-1-Ball-1: Does the pin step to "Player-2-Ball-1" ? AAA = Yes, BBB = No.

Great, ipdb has a schema: http://www.ipdb.org/machine.cgi?id=1072 -> look at schema-6-from-the-middle-to-the-right: See ?

Wire-Yellow -> "Switch on Outhole-Relay" -> "Switch on Extraball-Relay" -> "Switch on Ball-Index-Relay" -> then a fork: Upwards is for "Step to next Ball", further to the right is for "Step to next Player".
When You have "BBB": Check the switches on Outhole-Relay, Extraball-Relay, Ball-Index-Relay (when You make the first points: this relay will start pulling and KEEP-ON pulling - means: when the pin wants to step to next ball / next player: THIS relay MUST be pulling).
When Yo have "AAA": The three (written just above) switches / relays are good -> we then must look at the "forked-off UPWARDS wiring" -> the "communication "Player-Unit <-> Coin-Unit -> Ball-Count-Unit Step-UP".
Greetings Rolf