Sounds like an experience I had some time ago with my '83 Sentra. I tried what I thought was everything, but it wouldn't start. Tapped the starter with a pliers, but still wouldn't turn over. Towed it to the shop --- Started right up!
I never found out if there was an intermittent in the Park switch or possibly the shifter wasn't fully in Park, but I could never reproduce the problem. I didn't think at the time to try playing with the position of the shifter, or to move it to "N". Have you tried that? Too obvious to try, I guess.
BTW, I drove the '83 Sentra until this year when a bad timing belt caused more damage than it was worth. I replaced it with an '05 Sentra.