Not everyone is fortunate as I was to work for a very nice family-owned Chrysler dealership, but we never hold that against you!
The first thing to do is read and record the diagnostic fault codes. Cycle the ignition switch from "off" to "run" three times within five seconds, leave it in "run", then watch the code numbers appear in the odometer display. If we're lucky, there will be a code directing us to the circuit or system that needs further diagnosis.
Do you have access to a scanner to view live data? A common cause of a crank/no-start is a failed crankshaft position sensor or camshaft position sensor, however, that will cause no injector pulses and no spark. Since you have spark, we can rule out those sensors.
I need to qualify that wondrous comment. I left the dealership in 1999, and at that time, both signals were needed from those sensors for the engine computer to turn on the automatic shutdown, (ASD), relay during cranking. That relay sends power to the injectors, ignition coils, alternator field, oxygen sensor heaters, and fuel pump or pump relay. The engine would stall while running if either sensor failed. I do know that by around the mid 2000's, a running engine would continue to run when one sensor failed, but once stopped, it would not restart. There are also some car models where the engine will start and run in backup mode when one of those sensors has failed. I do not know if that applies to the newer Chrysler products. I just do not want you to overlook a failed sensor just because I said that cannot be possible since you have spark.
From your description of the symptoms, consider checking for proper fuel pressure with a gauge. Do not rely on the "push-the-valve" squirt test. The timing chains on this engine are a complicated affair with guides and hydraulic tensioning devices. Just because it is a chain instead of a belt, do not overlook that it may have jumped time. The symptom you described is exactly what can commonly happen on the four-cylinder engines with a single camshaft, except you will find erratic spark from one ignition coil in the pack, and no spark from the other one. This is caused by delayed camshaft timing but the timing marks on the sprockets will be perfect. The fault code will be "cam and crank sync".
I watched a coworker struggle for over half a day with two cars at the same time that had crank/no-starts that defied diagnosis. Eventually, out of frustration, he pulled a fuel sample, threw it on the floor, and tried to light it. Turns out it was mostly water. The "fuel" put the match out. Both owners had just filled up at the same gas station.
Friday, January 26th, 2018 AT 6:15 PM