#1. The male connector always have broken solder joints. Besides that the basic failures are....

Digit always on (bright) is bad level shifter. Bad level shifter left too long will burn out the 100k resistor

Digit always off bad digit driver or burnt 100k resistor, usually resistor burns because a digit locked on.

Same segment of each digit on a single display is probably bad segment driver or bad 4543 decoder chip.

Digit counts wrong on all displays 1,1,3,3, etc. Try one display at a time. Still wrong count display BCD data issue between MPU and displays, connectors! If wrong count stays at only one display and connectors are good bad 4543 decoder chip

Gibberish random segments on all displays. Try one display at time. If you find one display effecting the rest that display probably has a bad 4543 decoder. Because the data is shared one bad decoder can muck up the rest.

Segment driver, level shifter, and digit driver are all labeled on the schematics

I remembered that Bally actually did make a step by step repair procedure. It is in the 560-03 pinball repair book and starts at page 46.

http://arcarc.xmission.com/Pinball/PDF%20Pinball%20Misc/Pin%20Repair.pdf

I honestly don't usually like probing around HV stuff tho. After fixing a few games with display problems you can usually tell what component is bad just by the behavior of the display, after of course making sure the connectors are good.