Programming the key ina 2000 Avensis

My situation is the following. I have the lost the remote control black key-the one with the buttons on it(IS THAT THE ONE WE CALL THE MASTER KEY).
And now i am left with only a grey key with which i can start the car and lock/unlock it not remotely though.
It is not a remote control key like the one i lost.

And lastly i have a black key that IT IS NOT PROGRAMMED and as a result i cannot start the car with it.
The dealer told me that the only solution is to change ECU sth that wil cost 1600 euros-a very big amount of money.

My question is if there is any way i can program the black key so i can start the car with it.

Thank you