Michael, test for fault codes first. Key on, off, on and read out the blinks. Tell us your code readout in a post and we will feedback your trouble area where you should look.
Sometimes, though, intermittents don't register a fault code in the RAM chip, so you need to resort to low technology:
You might have an intermittent with the primary power relay in the power module. Bypass all the electronics with a jumper from Batt + to Coil +. This will power your fuel pump and ignition independently of the power module protection system. If the car still is intermittent, run a second jumper from Coil + to Pump + right at the fuel tank. Also it helps if you can hook up a fuel pump gauge to the shraeder valve on the fuel manifold. You should get about 55psi at all times. If it dips, its your fuel pump. If that checks out, it helps to dynamically look at the ignition system with a scope, just like we did back in '62 with a Sun Motor Tester on wheels. I once saw an intermittent in the Hall Effect tripe wire lead and that fault never even showed up as a computer detected fault. Intermittents are a real bitch, aren't they?
Don't forget mechanical problems can cause intermittents. Mechanicals like sticky valves, low compression, etc. But mechanical problems are not likely to flash the engine check light. Your problem is probably electrical and blame it on the two hundred wires and 100 pin connectors that go every which way. Especially problematic are connectors in close proximity to the battery. Battery electrolyte is a killer of anything electrical; Chrysler knows this so they recommend grease impaction in the connectors. What a joke. Can you imagine what would happen to all those electrics if ever you steam-cleaned your engine? Your car would be immobilized FOREVER!.
Next time buy Russian if Ladas or Moskoviches are sold in your Country. They don't have all those wires to go wrong. In fact, over there in Mother Russia, steam-cleaning their motors is a national pastime.