Probably it's a low battery, though it could be a bad starter. You are probably hearing the starter solenoid clicking.
One or both of you're drive axle bearings is dry
Bad axle maybe? Does it do it when you turn one way or another? Check to see if the cv boots are torn.
it makes that clicking noise because you touch yourself at night
central airconditioner makes a clicking noise when running? any idea what to check?
drive belts tensioner/under chassis
Fruit bats.
If the 1992 Dodge Caravan won't start but makes a clicking noise, it is probably a combination of things. The starter solenoid is making the battery go dead between starts. Replace both and the problem should be solved.
sounds like a bad wheel bearing
Where is the noise coming from? If its from the fenders or wheels is a much different problem than if its coming from the transaxle.
probably a wheel bearing
When you hear a clicking noise is most likely a battery problem however you stated that the battery was replaced so i suggest you check the condition of your cables look for rust or corrosion etc.
Sounds like a starter or battery problem, possibly wiring problem