If the battery drops close to zero when you turn the key on, your battery is probably finished. I would say it has an internal circuit that opens when any load is put on it. This is confirmed by the charger not being able to push any amps into it. If the battery internals are open it would be like holding the + and - clamps in the air....no current flow.
Try boosting your battery with a good car battery. Just don't start the car. If things come to life, you need a battery. If you still don't have any joy, continue what Ian suggested. Must be a connection, ground or positive.
