2005 Dodge Caravan Powertrain Control Module

I have a 2005 Dodge Grand Caravan SXT 3.8 Lv6 and the check engine light came on and after the local auto parts store code said miss fire detected cylinder number four probable cause bad plug. So we changed the plugs and wires. A few days later the light came on again and this time it was the EGR valve, we changed that and the vehicle ran fine for three or four weeks. The light came on again and we change the number four fuel injector and the light stayed on again and this it was the throttle positioning sensor, change that and the vehicle still ran the same, hesitating cutting out when accelerating and misfiring. So I brought it to the dealer and their diagnostics of the problem is a short somewhere in the wiring and they would take two hours to fix it. I just heard from them and now they are saying the power train control module is bad and we need to replace it. Can a vehicle run at all with a bad power train control module, could this be the problem? Any help in this matter would be appreciated.