Chrysler Repair: 2002 Town&Country electrical gremlins, electrical gremlins, starter solenoid

Question
I read through other's electrical problems but couldn't find one that fits my scenario.  I have a 2002 T&C and my wife went out to the garage yesterday to start it and it started right up.  She then realized she forgot something so she turned it off, went back into the house, then we she came back out the car wouldn't turn over, there was a loud repetative clicking from under the hood, and all of the gauges (tach, spedometer, temp, etc) starting moving wildly (flipping back and forth between zero and max), the front and rear wipers would come on by themselves (even the washer fluid would spray), and the parking lights would blink, though dimly.  After 30 seconds or so the car died down like it had a dead battery and nothing would come on.  She left it until I came home and it did the same thing for me (gauges moving, wipers on, etc).  I made sure everything was turned off and assumed it might be the battery so I tried charging it.  After 20 minutes or so the car came on and didn't act crazy, but still wouldn't turn over, with just the loud clicking (from the front left of the engine area when facing the engine)--only to slowly return to it's "possessed" state.  I called a tow truck to have it taken to the dealer, and just out of curiosity ask him to try to jump it (I own a Prius so couldn't jump it myself).  It started right up and idled for a few minutes perfectly!  Figuring it must be the battery, we left to get a new one only to go about 100 feet before the car completely shut down.  Same symptoms as before.  It's now at the dealer and they're looking at it, but do you have any ideas what might cause this "possessed" behavior, with everything turning on by itself and moving erratically?

Answer
Hi Michael,
I suspect that there is a short/loose battery connection of some sort that is draining the battery so the voltage drops to the point where the starter solenoid will not close firmly (the loud clicking sound) and that all the other things occur because the voltage levels surrounding the body computer and the digital data bus lines are subnormal. With nearly all of the electrical circuits that involve the body (as opposed to the engine) being mediated by that computer, if it is trying to operate with sub-par voltages these sorts of strange behaviors are the likely result. I would be interested to learning the results of the dealer shop's efforts.
Roland