Got my 2013 Edge battery dead, by inadvertently leaving the parking lights on all night. When I tried to unlock the doors with the remote, there was not enough power left to unlock. Then tried the key, but still could not unlock the door. Had to call a towing to unlock the vehicle, then boost to restart. Only explanation I can think of, is that by trying the remote, it slightly moved the mecanism, jamming the key lock.
Watch this one. If you get your battery dead, don't try the remote or key pad. Use the key first.