2000 Dodge Neon starting

Hi dawson1961 and TY for the donation

Park and Neutral switch is just to prevent the vehicle from starting other than P/N position it will not cause the engine to stall.

This problem could be caused by the following the idle air control motor, throttle position sensor, manifold absolute pressure sensor, also check the ignition timing and fuel pressure

Double check the battery and connection if okay

Check fuse no. 9 30amp if okay have helper hold key to start position and check for power at the starter motor small terminal brown wire -do you have power? If so it points to a bad starter if not swap or replace the starter relay and tell me what happened.

Check and test the P/N switch see below if it checks out it coming from the ignition switch

TEST
The park/neutral starting switch is the center terminal of the three terminal switch. It provides ground for the starter solenoid circuit through the selector lever in PARK and NEUTRAL positions only.

To test switch, remove wiring connector from switch and test for continuity between center pin of switch and transaxle case. Continuity should exist only when transaxle is in PARK or NEUTRAL.
Check gearshift cable adjustment before replacing a switch that tests bad.
REMOVAL

Unscrew switch from transaxle case allowing fluid to drain into a container. Move selector lever to PARK, then to NEUTRAL position, and inspect to see the switch operating lever fingers are centered in switch opening.
INSTALLATION

Screw the switch with a new seal into transaxle case and tighten to 33 Nm (24 ft. Lbs.). Retest switch with the test lamp.
Add fluid to transaxle to bring up to proper level.
The back-up lamp switch circuit is through the two outside terminals of the three terminal switch.
To test switch, remove wiring connector from switch and test for continuity between the two outside pins.
Continuity should exist only with transaxle in REVERSE position.
No continuity should exist from either pin to the case.