Originally posted by GN Bob
As Rickracer said, check your neutral safety switch.
Try this next time it won't start:
With the key in the start position, jog the shift lever back and forth between reverse and back to park without letting go of the key, (foot on brake of course).
You can also turn the collar on the steering column below the steering wheel since I think it rotates when you shift into park from drive. Try turning it further into the "shifted into park" position.
If the starter kicks, it could be that there is some slop in the mechanism that moves the safety switch fully to the start position when you shift into park. It is located at the base of the steering column and a bit of a bitch to get to & adjust.
Also try starting in neutral and/or shifting in & out of neutral to drive to see if the starter kicks.
Adjusting this switch solved my problem.