Ok... some basic stuff is needed before it gets a bit complicated... lift up the playfield and make sure that when you push the bumper ring down, the leaf switch underneath makes contact... the base of the ring sits inside a spoon.. this then presses down on the contacts.
Same with the flippers.. look at the contacts on the flipper buttons and make sure you have contact when flipper is pressed.
ALL coils on an em work on the same voltage circuit.. so if slings work, so should everything else. Check to see if you have voltage with a DMM
If all this is OK, then we need to probably look at some relays
