So, to my dismay today, I have run into the exact same problem. Touchscreen and steering wheel controls work perfectly, but none of the push buttons respond at all. I attempted a reboot by disconnecting the battery and it did not fix the problem. I then tried to access testmode by using the home button hold while starting the car. Still no response.
I found this thread. I see it is a year old, but was wondering if anyone has run across this since and found a solution.