There is a system that prevents the shifter from going to R and P when the car is in motion, I dont know exactly where and how it works but its there alright. Maybe its jammed or sticking.

In your model there are 2 cables on the shifter box too, one connects to the brake pedal and one goes to the ignition switch, its the park/brake interlock, meaning that it prevents the shifter from releasing from Park unless you press the pedal and the key is also not released unless the shifter goes to Park.

That maybe sticky, and you might also have coins in the shifter gate causing binding.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)