Neon won't start

there is a keyless entry control module

try starting it in neutral

If the headlights and dashboard lights are working but the vehicle still does not start, the ignition switch is most likely the problem. or a bad wire from switch. If your battery checks out, but the starter is still silent, it may be a faulty ignition switch. Turn the key to the on position (not all the way to start). If the red warning lights on your dash don't light up (and your battery connections are clean), the ignition switch is bad. If they do light up, turn the key to the start position. The dash warning lights should turn off at this key position (most cars). If you're not sure, turn on the headlights. When you try to start the car, the lights should either dim (a lot) or turn off completely. If they do, your ignition switch should be ok. If not, the switch will need replacement. check the wires to starter and see if you have power when car is switched on, do this first! good-day! if it cranks but does not start. check to see if spark and fuel, and check all fuses also.

tell individual working on it to check the crankshaft sensor voltage and signal when it wont start also check the fuel pressure and cam sensor, these are all possible problem with that particular car. it also has wiring issues that an expert tech would have to diagnose

The security system of your car needs to unplug or changed.

Read this and re-post your question with more helpful information. This one doesn't cut it.
Car won start Ricks Free Auto Repair Advice

If you have not already done this, try checking the clutch safty switch. On the upper clutch peddle assembly. Hope this helps.

i have worked on a neon before that had that same problem.so check the connections to your brake lights,stop lights,reverse lights,and turn lights.they could have a bad connection and its draining the battery.that was the problem i had so maybe your having the same exact problem.it had took me weeks to find that problem.i would jump start the car and it would run fine,let it sit for a couple of hours and the battery would be dead.so anyways ya check that i can almost bet thats your problem.

try starting it in neutral once,
then check the starter relay,then with a test light check for power at starter solenoid while someone tries to start it,

My Neon was doing the same thing. After hours of trouble shooting it turned out to be my positive battery terminal. It looked good but after replacing I have not had any problems.