I have a 2015F350 with the same problem. It's been doing this for months and nobody knows how to fix, not even a mechanic. Please help!

 

A quick search and ...

Transmission Stuck in Park

Left truck running, went in the store, came out and truck would not come out of park. But the P on the dash was not lit up like it should be when the gear is selected. Turned key on an off a few times, the P started flashing a little and finally stayed on long enough for the truck to start back...

www.powerstroke.org

 

I initially thought it was the neutral safety switch. But, it's located in the pan of the transmission and since it seems to be electrical, I dismissed that diagnosis. If you pull the cover off the shifter, inside you will see an inverted torque nut. Just below there is a plastic round disc. If you reach down the inverted nut, with your finger on the side closest to the engine, you will feel this disc. Pull the disc out towards the shifter, and you can switch gears...out of park. This will get you moving if stuck in a bad spot waiting the 20-30 minutes for it to reset. You can also wiggle the brake pedal and it might illuminate allowing you to start.

Now, there is a "stop, neutral switch" under your brake pedal. Replace this switch and your problems solved. It's about $20 and easy to do. I have had this thing at the dealer, another mechanic shop, and my dad has been a mechanic for 42 years. Nobody has figured this out. I have done this today and no problems yet. I will update in a few days.
2015 F350 Motorcraft part #SW7810

You can check if this is working right by starting the truck and pressing the brake pedal. You should hear the shift lock solenoid clicking as you press the pedal. If it doesn't click, wiggle the switch and wiring to see if it does. Believe it or not, this stupid little switch will lock you out of your truck. I have been dealing with this for 6 months. Please post your results!

 

Anyone ever figure what was the cause or part failure??. I have a 17 F250 as well and doing exact same thing...So irritating. If it's something simple I'd rather order the part myself than take to dealer for weeks.

 

UPDATE
So just got mine out of the dealer (3 weeks). With wait to get a diagnosis, parts ordering and the other waiting in line for completion. Painful but had to do it. Dealer replaced shifter cable and adjusted cable because bushing was worn and oblonged. But still had issue with the P and now R Flickering so they conducted another test (307-01B)... led to dropping Trans pan and replace the Trans sensor inside. Works fine now. Also shifts much smoother.
I also had the steering component recall performed while it was in. They replaced steering components w new and got an alignment.
Drives great now. Hope this helps someone too..

 

UPDATE
So just got mine out of the dealer (3 weeks). With wait to get a diagnosis, parts ordering and the other waiting in line for completion. Painful but had to do it. Dealer replaced shifter cable and adjusted cable because bushing was worn and oblonged. But still had issue with the P and now R Flickering so they conducted another test (307-01B)... led to dropping Trans pan and replace the Trans sensor inside. Works fine now. Also shifts much smoother.
I also had the steering component recall performed while it was in. They replaced steering components w new and got an alignment.
Drives great now. Hope this helps someone too..

Did your truck not re-start once you could not get it into park? Mine was stuck in P while running, then when I shut it off it will not start until it has cooled off. All the lights on the dash will flash and no start until cooled...