Not sure if there's a flow chart, but your approach is actually pretty spot on so far. Connectors and voltages. I'd probably start with the power supply board, you'll want to replace the electrolytic caps there. The bridge rectifiers can be tested with a dmm using the diode test. Coils under the playfield can be tested for resistance, typically anything under 2 ohms is bad (though not always).
It sounds like you have a few different things going on right now, so I'd start by rebuilding the power supply (electrolytic caps, check for correct fuses, etc) and connectors (re-flow/replace as needed for male and female sides). Once you have good voltages and connectors, you might find some of the other problems go away.