Gear shift stuck on park

I would say it has something to do with this !
Shift Interlock System An ignition/shifter interlock mechanism is installed to prevent shifting the transaxle out of the PARK position unless the ignition switch is rotated to RUN and the brake pedal is applied. The floor shift interlock system consists of:

• an actuator assembly integral to the ignition/shifter interlock cable assembly.
• a bracket retaining the actuator.
• the necessary wiring.

The solenoid is energized when the ignition switch is turned to the RUN position, locking the transaxle range selector lever in the PARK position. When the brake pedal is applied and the stoplight switch (13480) is activated, the ignition/shifter interlock actuator is deactivated and the transaxle range selector lever can be moved out of the PARK position.

Is the vehicle parked on an incline? The parking pin may be slightly jammed. If you can VERY CAREFULLY nudge the vehicle up the hill an inch or two, using another vehicle, the shift lever may free itself.
If the vehicle is parked on level ground, suspect the LOCKING SOLENOID for the shift lever.
Less likely, the parking pin may be jammed (inside the transmission), or the shift lever linkage may have become damaged.

What's your question ??????? Where do smell the burnt electricals ? Wiring harness burnt ? Fix it !
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This is a problem with the Interlock switch. Under the dash you will see the Brake pedal lever and it will have a switch on it. If this switch is hit by the drivers' feet it can be moved or broken. You can verify this problem by looking for the Brakelights to work when the pedal is pressed. If NO brakelights, the switch is the problem.

The cars are made that before allowing you to shift into gear, your foot must be on the brake. If the signal does not work on the Brake pedal, the car will not go into gear.

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.

your parking switch when out.open up shifter box there a locking device use your finger screw driver to unlock and shift the shifter.

Stuck in snow, if you spin the tires for a prolonged amount of time you can overheat the transmission and damage it internally. Without seeing it, my best guess is that's what happened!

Make sure you have brake lights.This is were the shifter solenoid gets it's signal from to get it out of gear.
One thing you can try is turn the igntion switch towards the run postion stopping just short of activating the electronics.Then try and move shifter to neutral then you can start it and out it into gear so you can drive it to get it fixed.

what year and model is the vehicle and is the shifter on the floor or steering column?

when you say it wont shift out of first gear what do mean it stays in first the whole time or it goes into like a nuetral state