Doubtful. Chrysler pumps rarely quit once they're running. They usually fail to start up when the brushes in the motor are worn. Backfiring is caused by fuel being ignited at the wrong time. That means you gotta have fuel.
Start by checking for diagnostic fault codes. Check for spark and fuel pressure. Fuel pressure can be misleading in this case. If spark is missing, suspect the crankshaft position sensor first, but don't go replacing random parts until they are properly diagnosed.