Probably it's a low battery, though it could be a bad starter. You are probably hearing the starter solenoid clicking.
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
check your battery then the connections if it still wont start try changing the starter solenoid if possible
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.
Dead battery? Maybe if it makes clicking noise -dead battery
Check your battery.
Does the engine turn over and then make the clicking noise while trying to start, or does it not do anything but make the clicking noise when you turn the key. If its not turning over at all then it might be a battery problem, Try cleaning the battery terminals, and/or charge the battery, Could also be the starter solenoid, but start with the battery first.
sounds like a flat battery
Charge or replace the battery.
typically a clicking noise indicated that you don't have enough power from the battery to turn the starting motor. try cleaning the battery terminals with baking soda and water, then charging the battery. dirty terminals or a dirty battery top will drain the battery causing starting problems.
You either have a corroded or loose battery cable connection at the battery, a defective or drained battery, defective starter relay or starter.