I would guess nuetral safety switch.

I have had so many go bad I just made a jumper to ground out the tranny NSS wire. You just got to be carefull to not start it in gear.

Try just a jumper from a ground to the post on the starter relay that takes the NSS wire...brown wire IIRC. If it starts the switch is the problem. Either the switch is bad or something in the tranny is a bit out of alignment when in park.