help, remote key programming problem
 

Hello
First of all, I ask for your understanding because I am not good at English.
I have only one remote key.
So I bought used remote key as same part number.
The purchased key emits a signal (operates). and frequency is the same as existing key.
But only the existing 'already registered(which was in use before)' remote control key is re-registered.
I also tried several times to reset the ecu and battery.
Also, I tried to find various ways, but I failed. (youtube and forum topics)
It also impossible to register as OBD machine and key programmer machine.
It also failed at a private key shop(specializes in Audi)..
What's the problem? Can you guess what the problem is?
What kind of method can I try? vag-com? Official service center(dealer)?