First of all I dont think anyone can fix a "smart" key, since they dont have the equipment, unless is is a cold solder joint on the board. I also question how they were able to test it. If you charge the battery the key should register and work. The key communicates and gets its energy via a reduntant DAS data path and gets its power from the steering collumn. I would call the customer and have them bring down their spare "smart key" if they dont have one. The third option would be for you to go to your local MB dealer and purchase an "additional" smart key, and since you dont know which one you have, ordering a "replacement" will void one of the keys, and might result in waiting up to 45 minutes for the new key to erase the old and register the new one.
A new one is less than $200.
The door unlock is infra red (batteris in remote), the key is inductive energy from the collar.