Gear shifter stuck on P. Won't move, and button, 1994 El Dorado

Could be the brake switch or the shift lock solenoid. You may be able to turn the key lock to the unlock position, move the shifter out of park, then start the engine in neutral.
The shifter and the shift lock solenoid would need to be inspected.

The first thing to do is check the brake lights, it they are not working the park lock system will not release the shifter.

Rock the car back and forth to remove parking pin from park .

there is a release solenoid triggered by a brake switch

Try shifter cable

replace shift control or button on shifter

Ignition - Key Stuck In Ignition Switch/Won't Turn Bulletin No.: 06-02-35-005 Date: February 28, 2006 TECHNICAL Subject: Key Stuck in Ignition, Key Will Not Return to Off Position, Shifter Button Won't Release in Park Position (Adjust Shifter Detent Finger) Models: 2002-2005 Chevrolet Monte Carlo Condition Customers may comment on any of the following conditions: - The key is stuck in the ignition cylinder. - They cannot return the key to the off position to remove the key. - The shifter button won't release in the park position. Cause This condition may be caused by the detent finger shifting over time. This may result in mis-alignment and binding of the shift rod on the shift position guide.
WHERE YOUR SHIFTER IS YOU WILL HAVE TO TAKE IT APART ..MAYBE THE RUBBER BOOT IS IT THE WAY,OR THE SHIFT LOCK SELINOID WHENT BAD

check the fuses as if the brake light fuse is blown it won`t allow the shifter to move out of park.it has a shift interlock system so the gear shift won`t accidentally be moved out of park by mistake.

There is a small plasic acess cover (1/2" x1/2") on the base of the shifter. Pry it open and press the button. You should immediately be able to shift. The button is needed because the sensor on your brake pedal is broken (won't activate your brake lights either). Use the button on your shifter to get your car home or to the mechanic so you can get the brake switch fixed. Remember whern you drive you have no brake lights. -Mark

my car got stuck in park several times, i'm the brake lights would come on but i couldnt push the button to make my car move out of park...there's a tab on the right side at the top of the gear shifter console pop it out, stick a skrew driver down in and that should release it if that's your problem...it's a little bit of a rig, but it works, havent been stuck in park since