The key point to this question is that the battery goes dead!!. The clicking noise indicates a weak battery because it does not have enough charge to keep the relay/solenoid held in to engage starter. Try to get a jump, and if it starts, let engine run for about 10 minutes while driving or fast idle. Shut down engine and see if it starts, if it does, then check voltage with volt meter across battery terminals. It should be 14.5 or 15 volts. then shut down engine and it should read 12v - 12.5v. Make sure battery and starter and solenoid terminals are clean and tight. try again an hour later. If same thing happens, your battery is probably no good, because when it was running, the voltage across battery was 14.5v, meaning that your generator is charging.
drive belts tensioner/under chassis
I don't know what "after battery is off" means, but if it is clicking while trying to start, then most likely the starter/solenoid/relay is bad.
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.
Clean or change wiper fuse, check battery
check your battery then the connections if it still wont start try changing the starter solenoid if possible
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.
Probably it's a low battery, though it could be a bad starter. You are probably hearing the starter solenoid clicking.
Charge or replace the battery.
A dodge caravan may be experiencing rear brake noise due to needing new brake pads. This may also be due to worn rotors.
Try cleaning the battery cable connections of corrosion.
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.
Is the battery fully charged? Try jump-starting it.