Dodge neon 2002 need help

Standard transmission? Auto transmission? Possible shorted neutral safety switch

Does your key switch work good? Do the warning lights and gauges on the dash all turn on with key in on? That verifies the ignition switch has power. If not, check fuse #9 in the Power Distribution Center (under the hood). It is a 30 amp fuse, providing power to the switch.
Are the battery cables clean and tightly connected at the battery and starter and the battery ground connection?
There is an Engine Starter Motor relay in the Power Distribution Center, the only thing between the ignition switch and the starter. With key in start, power is sent from the switch to this relay, and if relay is activated by the PCM (engine computer), then power goes on to the starter solenoid on the starter, and starter should then operate and crank the engine. If you have a voltmeter, you could do some tests for power at the terminals the relay plugs into. There are only 4 terminals. Post back with comments, or if you need help with testing those terminals.

Is it getting fuel? Check the pressure regulator or the fuel pump. Even if you have the plug wires on wrong it should do something.

Check that the immobiliser (if installed) is working correctly

Hold ignition in start position, and move selector back and forth in Park.

I had a similar problem where the battery was ok but there was no sound from the starter and also there no lights on in the dash when the key was turned. Checked the fuse and checked wire from the fuse back to the ignition switch. The wire from the fuse was ok in fuse box but had no voltage at the ignition sw. The was also no voltage to terminal 30 in the starter relay. Ran a new wire from the fuse to the ignition and it fixed everything. Check for voltage at terminal 30 on the starter relay

if it doesn't even turn over check starter cylinoid/relay, if so, check ignition fuses and relays.

Check your fuel pressure.
Possible fuel pump malfunctioning, check the fuel pump fuse and realey.
Check your ignition .

I was having the same exact problem with my 2005 neon as well. The guy at Discount auto suggested the starter itself was the problem(cost approx $200). The car isn't old enough to be having a starter issue so I figured it was something more simplilar. My dad took a look and founf out it was the starter relay. It is located in the black fuse/relay box on the driver's side right next to the battery. I had to get a new relay at the dealership(cost $20) and my car starts perfectly. Hope this helps

Have you checked the starter relay on the fuse panel? Hope it helps. Good luck

check the ignition switch or the nuetral safety switch