Had a similar problem on a dodge daytona. The way to check it on a daytona was to turn the switch on / off thirteen times without trying to start it. Then wait about 5 seconds and start. You must make sure all connections are making contact such as in the doors, under the hood, trunk.
because I didn't have the clicker I had the alarm system taking out and thought that was it. There was an alarm backup box ( that had a backup battery that could last from 6 months to a year) located inside the dashboard behind the glove box, had to remove the dash to get to it. It was very odd because it seemed as if the alarm would activate by itself, don't know if another car nearby, electronic store doors, aircraft, etc., would set it off.
This might cost you some $ to get fixed. Air, fuel & ignition, you have to have all 3 to get running. Find out which one is NOT happening. My guess would be ignition. I would head out to an AUTO ELECTRICAL SHOP and have them go over the car.
You might want to try to find a SHOP MANUAL on this car. One with a wiring diagram. It will take some looking.
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