I have a 2010 QX56 with similar issues. My ac/radio was working fine then it went to a intermittent on/off and finally just stopped working all together. My display screen works fine but when the ac/radio was going out it would revert back to what looked like was a default setting on th ac temp because both driver and passenger would be set at 72 degrees and you could hear that it was on but could not control anything on the ac or radio with the exception you could control the radio volume with the one on the steering wheel but that was it and you could still turn on the rear ac controls. Took it to dealership and they said the ac/radio would have to be replaced so I did with a very lo mileage one from salvage yard that was practically brand new and it still had the same symptoms as the one I had just taken out. Done a lot of research and a lot of people have had similar issues but then again most are having the display go blank and mine does not. Found it could be anything from bad resistors in radio coming lose due to bad solder job to replacing BCU and AV Controller. Oh yeah checked all fuses and even put fresh battery in it as well as checked for codes and found nothing pointing at the issue at hand.I have even took the battery cables off for an hour as well as touching the positive and negative together to reset the BCM then reinstalling cables with same results. I just went back to the salvage yard and got the BCM out of the lo mileage QX56 but all the sudden my local Nissan service dept says they can't program it because it's a Infinity after they initially said they could. Any insight on what this issue could possibly be would be greatly appreciated.

I might be wrong but I believe the only thing that a BCM needs to have programmed is for the key programming, which most locksmith places can do, I suggest you look into this.

Maybe try installing the new BCM and see what happens I doubt you can mess anything up.