Sounds like you just need to understand how the system works. The Engine Computer turns on the automatic shutdown (ASD) relay for one second after you turn on the ignition switch. That sends voltage to the ignition coil, injectors, alternator field, oxygen sensor heaters, and fuel pump or pump relay. That is probably what you're seeing when you have voltage to the ignition coil. The ASD relay turns off after that one second, then the computer turns it on again during engine rotation, (cranking or running). It knows that by the signals from the camshaft position sensor and the crankshaft position sensor.
The first thing to do is read and record any diagnostic fault codes unless they were erased by disconnecting the battery. Chrysler makes doing that yourself real easy. Cycle the ignition switch from "off" to "run" three times within five seconds without cranking the engine, leave it in "run", then watch the numbers show up in the odometer display.
The next thing is to determine if the ASD relay is turning on during cranking. It sounds like you were already doing that. Monitor the voltage to the ignition coil or any injector. You should see 12 volts for one second when you turn on the ignition switch, then again during cranking. If it doesn't come back during cranking, the signal is missing from the camshaft position sensor or the crankshaft position sensor. The most common problem is the crank sensor got smashed during engine removal or reinstallation, or a new spacer wasn't used to set the critical air gap.
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Thursday, October 4th, 2018 AT 10:34 AM