It sounds like the radio itself has gone bad which is a common problem. I would replace it with an after market or a used unit.
In the case of radios, there is no legitimate reason that radios and amplifiers have to programmed to work, but designing them that way means more money for the dealers. They also will not allow us to buy radio service manuals so you're stuck with the dealer and their grossly over-priced repair centers. In the case of BMW, they will not release paint codes to independent body shops, (they have to buy their paint from the dealers), and they won't even release service information to the general public. None of those practices have the customers' best interest in mind.
As for your problem, the first repair did not solve the problem so the ethical thing to do is remove the new part and re-diagnose the problem correctly. The dealer is the last resort for getting things fixed, and they should not be guessing at the cause. Tell them you want the problem fixed correctly, and if they can't you'll be happy to share that with friends and coworkers.
Please let us know what you find so it will help others.
Best, Ken
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Saturday, February 18th, 2017 AT 4:16 PM