Going to reiterate this and hopefully you confirm that I read it right.
You unplug battery and reconnect.
When the key is turned to on, you have lights and things seem fine.
When the key is turned to start, you have no lights and hear no fuel pump, then when you let the key fall back to the on position there are no lights and no power to car.
Unhooking the battery resets things and you go back through the cycle.
That's right? If so, please check that when you are hooking up the battery the connections are good and snug. The cable connection to the battery isn't corroded etc.
Has any work been done to the car in the last ... 3 months?