Remote won't program on Lincoln MKS 2011

I bought a Lincoln MKS 2011 with one key fob. I can start the car and open it manually by
using the heat sensor on the door, but the remote buttons don't work. I bought a second
remote ($150) and took it to the dealership. They charged $100 and said they cannot
program the remote. They said that something in the car is probably broken. They need to
run a diagnosis for $120 and then I might need to replace a part (wireless module maybe?)
and then try to reprogram it again.

So far I'm $370 in.

Does anyone know what the reason behind non programable car is? What could be broken?
So I have an idea what expences to expect.