There are 2 paths here:
1. The (blue) path that contains the Credit Button
2. The (green) path that starts the score motor
check each path to see if any switches are not adjusted correctly.
I cut out things you don't need to see from this image. Do you have a schematic?
Since you mentioned the coin drop I would think the coin chute switches need scrutiny first. If the NC sides are not closed power cannot flow