the board pins probally need to be reflowed.

Before you cook your displays, do you have meter to check your display voltage?

Awesome .. congrats ..I'm not jealous .. honest

i found this really helpful with reco of mine.
http://stevekulpa.net/pinball/bally_disp6r.htm

As Vid said, check your display voltage. I would suggest starting at the rectifier board, then solenoid driver after that. If your voltages are okay, then check the upper left connector on the CPU board.

http://www.pinball.yoo-design.com/download/pdf/schem_solenoid-driver.pdf

bottom right corner

I had a similar problem.

I used this guide to troubleshoot:
http://techniek.flipperwinkel.nl/ballyss/rep/index3.htm#display

Scroll down to section "3n When things don't work - High Voltage section problems".
The photo shows the high voltage section of the solenoid driver board. Under that plastic line shield is a tiny 8AG fuse. This fuse protects the high-voltage side of all displays. I'm suggesting this as another place to check while you're looking.
Just as a reminder, you need to remove at least one end of the fuse from the fuse-holder to properly check for continuity on fuses (just in case you weren't already).

The above article has a really good walk-through for checking the power supply, rectifier board, and other items. Your troubleshooting method appears to be sound. Start at the source - where voltages are derived. Chase through the system until the fault becomes evident.

I'm glad that little fuse solved your problem (mostly)!

A 1/4 amp fuse is a touch too large. Yes, your displays will work but they are over-fused and exposed to risk of over-current. I used a 1/4 amp fuse temporarily for troubleshooting but I really don't recommend this practice. Get the right one installed ASAP.
This site has your fuses and many other parts:
http://bigdaddy-enterprises.com/

Still talking about your displays. The missing digit is an easy fix. I used this article to track down the offending parts:
http://stevekulpa.net/pinball/bally_disp6r.htm
Scroll down to the part dealing with the level shifters.

As for playfield coils:
Use the flipperwinkel guide I posted above. Section "3i" will get you started. If it were me, I would start at the rectifier board. I have a 1984 system so it may be different.
If we have the same board (AS-2518-54):
You should find +43vdc between TP5 and Gnd
This circuit is protected by a 5A fuse labeled "F4"
Hope this helps.

Another handy thing to use while troubleshooting your coil circuit is to rig up a circuit breaker (sized appropriately for your circuit). Much better than "smoking" fuses while you look for a problem. Also, don't risk using too-large of a fuse while troubleshooting. You're likely to "smoke" something downstream and create a much larger problem.

3/16 = 0.1875
1/4 = 0.25

Close enough in my opinion. In fact i always use a 1/4amp or 210 mA fuse because 3/16a is hard to find. Bally didn't even fuse the regulated side of this circuit on the first generation boads. If the HV transistors short this fuse won't even blow and +230v goes right to the displays (bally design here is stupid).