In a 2013, you still have the vehicle that is NOT keyless start (the button) instead it has - Key in the Ignition?
Then the "can't remove the key unless the thing is in Park"
And if you were able to remove the key.
Means the issue of the range switch - and the column that holds the key and the mechanism that uses the shifter - a linkage - that then moves a clip/tab combination in the key housing to release - letting it turn all the way to Off and releases the key so you can take it out - even that tumbler that the key moves in, could be damaged.
This "stuck in Park" problem is really a cascade condition. The shifter has to move a lever - to operate a linkage, so the Key once in the tumbler is turned from "Off" - is now locked in - and to remove the key - the shift lever has to physically move a linkage to release a tab that lets you remove the key.
You said this...
Brake pedal doesn’t push down hardly at all when this happens
Ford did various combinations of that tab, up to and including using a relay to move a solenoid that unlocks the shifter "release" lever - so be ready when you take apart the shifter and the steering column - to look for the ways that Ford did use up theft resistant lockout hardware using shifter linkage so you can remove the key is part of this method - find what they used - so you can fix it. This is a de-evolving of what Ford/GM/Chrysler used to have to have in the vehicles. As it was a steering wheel lock that keeps the wheel locked when the key is removed - back in 2004 GM got sued over this - so all the makers had to remove that lockout. Your (everyone else included) vehicle now had all these orphaned parts. In Ford's way of using up parts that it won't need anymore that it wanted to use up and not throw away - used these parts in various ways to use up the inventory.
- Your stiff brake pedal is a strong clue to this - the linkage needed to release the Park lever uses the Brake pedal - one of the switches - so one of those switches can be faulty - sticking out - jammed - keeps the brake pedal from going all the way back to retraced resting spot.
- So the valve that the brake booster uses to close and apply vacuum to power assist the brakes - is left open and so it leaks air in - after enough time - there's no vacuum, so the pedal feels dead. That means all the vacuum boost it once has is gone and the brakes are "manual" the pedal is resting on the Master cylinder pushrod with not boost in vacuum to assist the pedal to move further down.
- The booster vacuum is a restriction port - and the valve - to keep people from over applying the brakes to prevent wheel lockup and accidents - the valve is a small port to let air in The pedal, when pressed, lets the valve open the port, air goes in, and the vacuum chamber pressure differences are what applies the extra downward force of pressure to apply the brakes - you feel the effect in the pedal as it travels.
You don't have to take my word for it, you'll find you'll have to remove the steering wheel, the shifter cover in the console and all the trim to expose the key tumbler - the linkage and follow it to the Shifter, thru the center console - to locate the method of either physical link to clip to tab - or they used a relay - solenoid combination..
Once you understand that - the issue of trying to locate where NEUTRAL is, or the TCM switch that follows the linkage of the shifter then becomes more clear.
IT's the YEAR that is was made, the switch could be fine, the physical aspects and design and materials used to operate the switch - might not be.
The whole mess above - is a reminder to me, of why I switched to Manuals.
