My mercury mariner starts fine but wont shift out of park. Mostly only does this after sitting awhile, it's a 2006 model year with center console shift. The shift button on shifter wont depress.

Make sure that the linkage is correct. It may not be engaging all the way into reverse

Have it aligned and tires balanced. If the tires are not in good shape replace them.

Tom, there is nothing elise it could be but motor and or trany mounts

Check your brake light function. If that is at fault then your brake light switch may be faulty. If your brake lights are fine then you may have a faulty shift lock solenoid. Some Japanese models of that era have a button or key slot near to the shift lever. If you depress that then it should manually release the lock and allow you to move through the gears, until you move back to 'P' position at which point it will lock again.

there are 2 reasons.
1: park lock out is broken (brake switch activated)
2: or the tires are jammed in to a curb, going down hill,
(known as parking pawl lock up , inside the tranny)
(is car on flat ground?)
you never said what car, just jeep and they made jeeps from 1941 to now. so cant guess.
what jeep?
many jeeps, have a hidden super secret (in the operator guide under how to drive a A/T)
secret bypass. lever on the shift console.
so post year, and model of jeep and we can dig that up.
or go to alldata.com , log in and read, the park lock out page.

When parked on an incline, engage emergency brake FIRST, then shift into Park. Hope this helps! Works for my Buick.

HAVE VECHICLE CODE SCAN.SOUND LIKE YOU COULD HAVE BAD WHEEL SENSOR OR DISCONNECTED OR LOOSE WIRE.BECAUSE 4WD DRIVE NEEDS SIGNALS FROM WHEEL SPEED SENSORS AND VECHICLE SPEED SENSOR BEFORE AUTOMATIC TRANSMISSION AND TRANSFER CASE CAN SHIFT CORRECTLY.

water pump-
crack in the housing from sitting over the winter with water in it

sounds like a bad ingition coil