Chrysler Repair: Park Netural Switch/starter relay: 300M 99, neutral safety switch, starter solenoid

Question
1999-300M with 140K miles.  1 out of 20 to 30 times when trying to start will do nothing.  No solenoid clicking.  My first guess is P/N switch second guess in ign. switch.  Will start normally after 2 or 3 tries. Battery new and OK.  I'm not sure how to get to the P/N switch can you help?  Could there be a third choice of this problem that I've over looking?

Answer
Hi Rooger,
The start neutral safety switch is inside the transmission at the end of the shift rod that goes inside the solenoid box, so you could trace that when the starter motor refuses to engage. The wire is black/white on pin 9 of the 10 pin connector at the solenoid box, and it should be grounded when you are in P or N. This wire then goes to the powertrain controller at pin 76. Then the controller should ground the far end of the starter relay's actuation coil in the power distribution center (pin 31 tan/white to pin C of the relay. The ignition key provides the 12V to the other end of the relay, pin A in the start position. So when you don't get starter motor, find a helper to operate the key and listen/feel for a click of the starter relay, and if there is no click check to see if A has 12v on it which comes from pin 9 of the ignition switch on a yellow wire.
Thus you can verify if it is the ignition switch or the trans sensor switch, or the relay, or the starter solenoid if the relay is good. The power for the starter that is controlled by the relay comes on pin B on a red wire and goes to the starter solenoid on a light green wire from pin D of the relay.
Let me know what you learn, please.
Roland