Well we can narrow it down a bit which helps to begin solving an issue.
...machine starts OK, adds credit Ok when coin contacts are closed, but goes cranky when start button is pressed.

Seems to me the RESET is out on this....... score reels set to zero but then continue.

Score reels turn and zero point is normally registered... having said that this only occured once the PF was dropped, it would probably be wise to rule out contacts in the header for now.... id be looking at the RESET relay... make sure all contacts that should be touching are etc... this would in turn talk to the START and 1ST BALL relays... same again.. check contacts