Help! Key turn kills the entire electrical system - all lights go off, no crank.

Hi all,

About three weeks ago, I left my lights on overnight and killed my battery. The battery was 100% dead -- no cabin lights, no cranking of starter, no clicking, absolutely dead. The battery sat dead for about 2 weeks until I recharged it with a battery charger.

Tonight, I went to start the car. The cabin lights came on and the doors unlocked electronically upon pushing the keyless entry button.

I turned the key, and everything went off -- all cabin lights, etc. No starter cranking/spinning/clicking.

I got out of the car and shut the door and all the cabin and dash lights came back on. The OBC said "Input Time."

I repeated this process about three times....sure enough, the cabin lights came back on each time I got out and shut the doors.

What on earth do I do? This doesn't sound as simple as just replacing the battery....