Thank you for your pronp replies. The door thing with your son is just a fluke coinsidence here then. You have a bad battery, have the unit charged and tested to be 100% sure but the rapid clicking and dash flicker is low power, basically the battery has some power to activate certain things but when you turn to "start" the rapid clicking you hear is the starter solenoid cycling.
Time for a new battery, I highly recommend an interstate battery if possible.
Age doesn't matter, I get brand new batteries that do this. You either have a crappy quality/brand battery (no offense) or this is just a dud. You stated you drove the car home and it immediately would not restart, this tells me: 1- the alternator is working properly and 2- the battery is NOT taking a charge and has a bad cell.
Sorry but it's time for a battery. I have been in the automotive business for some years now, I have found that interstate batteries have the best price/reliability/life and value, HIGHLY recommend one if available. Aviod batterys from wal-mart, parts store brand batteries such as NAPA/advanced/car quest, they usually only last about 1 year.