98 Dodge Avenger starter

Did you install a used starter? Worn solenoid contacts are very common on the little silver Nippendenso starters. They will usually test good off the car because very little current has to get through those contacts when it's not loaded down by turning the engine. The symptom on the car will be a single kind of loud clunk from the starter but it doesn't spin the engine until you cycle the ignition switch repeatedly.

If that's the symptom with a new or rebuilt starter, measure the voltage on the larger wire on the starter while a helper turns the ignition switch to "crank". Holler back with that reading.