I have a 2005 Neon SXT automatic with 176,000 miles on it. I have had it since 34,000 miles and it has been a great car.

Recently I got in it and when I turned the key all the lights on the dash lit up, no codes, but it wouldn't make a sound. No click, no whir, no buzz, no noise. Turned out to be the starter so I replaced it. It ran for about 3 weeks then did the same thing. I removed the starter and had it checked and it passed. I checked fuses in the dash and the ones under the hood and they are all good. I jumped the starter from the battery and it will turn over, but not start even with the key on. I removed the gearshift cover to make sure all the cables were connected and nothing was broken. I shifted while looking at both sides of the hardware and everything looks good. I swapped the horn relay(horn works) with the starter relay and the horn still works and the car still won't make a sound. I took the relay apart and probed the pins following some instructions I found and all the pins operated correctly. When probing pin 86, the car will turnover with the key turned on or off, but still won't start.

Any ideas on the next thing to check? Can the computer be checked if removed from the car?

 

I thought the next things I would need to consider would be the ignition, neutral safety switch, or computer. I have looked up the neutral safety switch, but I can't find anything that looks like the part looks on the parts websites. I understand that it should be on the transmission, underneath the airbox, on the drivers side front, behind the light. Am I overlooking it?

 

Dodge calls it a Transmission Range Sensor. It probably looks like the pictures you're seeing. The problem is that it is mounted on top of the valve body inside the transmission case, which means tearing the transmission apart to replace it. The only part that is out side the transmission is the electrical connector. Sounds like you're looking in the right place. It's a square connector towards the right side looking from the front. Have you tried starting the car in neutral? I bought an 05 Neon a couple of years ago to flip. Previous owner couldn't get it start so I got it cheap. Towed it home, dropped a new battery in it, but wouldn't start. Put the car in neutral and it fired right up. Disconnected the connector from the range sensor, sprayed some contact cleaner in it and never had a starting problem after that.

 

I tried to start it in neutral with no luck. It does the same thing whether it's in neutral or park. I am afraid is the comp, but the car is worth about what it would take to fix it unless I look online and buy the cheapest I can find and hope is not a ripoff.