I can't get my car out of park - 2009 Mitsubishi Galant

http://www.parkandgo.co.uk/heathrow-airport/

http://www.pickaparking.co.uk/Heathrow?gclid=CLi83a3nj8kCFYGbvAodZ0YCTA

https://www.simplyparkandfly.co.uk/Heathrow-Airport?gclid=CNXMrdfmj8kCFQuavAodz1QB2g
https://www.looking4parking.com/uk/airport-parking/heathrow/lhr?campaign=LHR&adgroup=CheapAirportParking&gclid=CIKt4Nvmj8kCFYmUvQod94sCJQ

http://www.parkbcp.co.uk/heathrow/airport-parking.html
https://www.essentialtravel.co.uk/airportparking/heathrow/long-term-parking.htm

I would make sure your shifter cable is intact and the transmission is actually in park. The safety switch is located on the transmission and if the shift cable is not moving the shift linkage all of the way into park the car will still roll, and will not start in gear.

parking, yes, tail ,park.
(the correct name is park toy calls them tail, tell me how a tail lamp works in front of car, this name is from 1920cars , that only had 1 or 2 tail lights. (fun history that, with funny names)

if actually park lamps. 1st click of head light? switch?
there are over 20 park lamps in car, inside and out.
side markeres, front park lamps
all dimmable lamps inside are park too. all dead>?
then the park relay is bad (tail/park) or fuse. blown.

park lock out failure? some cars have park lock out defeat lever
or insert key here, point, to release it.
never seen one fail to go to park from drive.
but no 2 cars are same in this regard, all use different mechanisms and and cables.
or the parking pawl is bent.
cause by going to park moving.
or are you down hill or on uphill parked to curb?
the parking pawl (in tranny) may be hard to engage, if you fail to move car just a tad forward or reverse.

all cars with A/T have 2 features, the parking lock in the tranny.
this is a lock up device.
and key on, off, brake on and off, park shifter lock out.
you must fist find out what is failing here.
the shifter or the tranny

if you have the operators guide, it tells you the console park lock out defeat, on every car i have ever seen.

neutral safety switch could be loose or faulty or transmission manual shift linkage is out of adjustment.

If your parking brake is too loose or is not properly adjusted, you may encounter problems while parking, positioning and driving your car. Most of the time, car owners would send their car to a mechanic in order to fix and tighten the parking brake. However, you can actually skip this step and adjust your parking brake yourself. When your car starts to slip on a hill in its park position, you need to start tightening the parking brake.1 Remove the car's center console cover placed around your parking brake level inside your car. This is found between the seat of the driver and the front passenger.2 Use your wrench to turn its adjuster nut found at the end of your parking brake's cable rod. Loosen the adjuster nut with your wrench, while making sure that it does not come off at your parking brake cable rod's end.3 Raise your car rear wheels using your jack, and use your jack stands to support both its rear wheels.4 Pull up your parking brake handle up to two clicks or notches. Tighten your adjuster nut until you feel a slight resistance on your rear wheels whenever you spin them.5 Release your parking brake lever. Check and make sure that your rear wheels are still able to spin freely and without any resistance.6 Pull up on your parking brake lever up to three to five clicks or notches, while making sure that your car's rear wheels are not turning at all.7 Lower the car by adjusting your jack, and remove your jack stands from your car's rear wheels.

The way to avoid this when parking the car on a hill is to apply the parking brake first, allow the car to settle in position by easing off the regular brakes, then put car in park. When it is time to go put the car in gear then release the parking brake. Let the parking brake do all the work. This problem is common to most cars with an automatic transmission. The weight of the car is pressing against the parking mechanism inside the transmission. Many folks have to resort to having a friend rock the car forwards and back to free up the parking mechanism.

Is your car Parked on a hill. Do you use the E-brake.
1st. Make sure you, press the bake peddle.
2nd.If the car is parked on a little hill facing up or down
you'll need to move the car a little. Up or down.
3rd. When the car is parked not level the transmission
parking PAW or PARKING lock inside the Transmission
may have to mush pressure on on it to move easily
So, that is probably the problem. Move the car eighter way
to relieve the presser off the parking Paw. When parking the car
when stoped, Leave your foot presure on the brake pedal.
set the E- Brake then put, the trans into PARK.This way
The presure, in the trans parking lock is not to tight.

The park pawl is spring loaded and it sounds like that spring has broken. The problem is, the trany has to be removed from the car and completely disassembled to fix it. The linkage for park is all mechanical, the transmission could be completely out of fluid and park should still work. I guess, I would get into the habbit of setting the park brake, then put the car in park and pull it out of park, before you release the park brake. You could also leave the shifter in the neutral position and set the park brake. This will allow you to start the car but you won't be able to remove the key. Hopefully the brake cables are not all rusted up. Good luck.