What in the world were you thinking when you told them about the dead battery?!??!!??!

You gave them the implement with which to screw you! Really silly to trust the dealer to take information and use it to diagnose- they use it to screw you.

How old is the battery? I think you'll have a new battery in your future- failure mode seems to be weird, unrelated errors as modules do funny things.

if you do replace it, DONT BUY IT FROM A BMW DEALER.

A