startup problems

I have a 1996 Maxima SE, which has been great except for some occasional problems with the electrical system. The first episode was in 1998 (still under warranty), when the entire electrical system went dead while the car was running. At that time, the alternator was changed. Everything was fine until a few months ago, when I have had more and more frequent difficulty starting up the car. The lights on the dashboard and the radio will turn on, but the engine has not been turning. Sometimes after waiting a while, or while pressing down on the accelerator, the engine will start. I have had the battery changed last year, and the alternator and battery have been checked recently by my Nissan dealer and a gas station (two separate occasions). Today, I couldn't start it at all while the gear was in park, but I could start it when it was in neutral on the first attempt.

Two questions:
1. Is there any long-term problem starting the car while in neutral gear?
2. What else needs to be checked and/or replaced?

Thanks for your help.

Your Park safty switch is bad. Nothing wrong with starting it in Neutral.