The Battery is shot and you need to replace it.
I have the same car with the same clicking noise right after you start the engine. The noise stops shortly after starting. There was a recall from Chrysler for this problem. Contact your local dealer regarding this matter.
If just clicking and not starting, most likely a dead battery.
A clicking noise in the engine of a 91 Ranger could indicate a problem with the valves. A valve lifter in the engine may be worn or stuck.
Possibly the lifters?!?
Where is the clicking coming from? Within the engine compartment or inside the car?
dead battery
If clicking while trying to start then might be a bad starter. If clicking while running, then might be valve/lifter noise.
clicking noise when trying to sart engine usually indicates a flat battery.if the battery is not the problem ,the starter motor needs repair.
You need to check your starter or your starter selenoid.
If the Chrysler is only making a clicking noise and will not start, check the starter. Also check the alternator, and the battery. The starter solenoid is more than likely the reason the car is clicking and not starting.
It does that when the engine is cooling off. It's called expansion and contraction.
That is lifter noise, they probably need adjusting