When the shifter will not move from Park, first, check your rear brake lights, and see if they are working when you step on the brake pedal.
If the brake lights are NOT working, the problem is going to be the Brake Light Switch, located at the top of the brake pedal arm. This switch controls the rear brake lights, and also sends a signal to the Shift Interlock, telling it to release when the brake pedal is depressed. Inspect the electrical connector for any loose or broken wires. If the visual inspection checks ok, replacing the switch will solve gthe problem.
If the brake lights ARE working, then the problem is going to be a broken spring internal of the shifter assembly. This is actually a HUGE problem for Dodge/Chrysler, and they have issued a Recall: #K39. The problem is a broken spring retainer internal of the shifter assembly. The recall will have them remove the shifter assembly, and "rebuild" it for you, absolutely Free. Unfortunately, due to the location of the break, not even the "over-ride" procedure will work.
Here is the "official" word from Dodge/Chrysler:
Customer Satisfaction Notification K39
Transmission Shifter Interlock Lever
At Chrysler Group LLC, you can be assured that we are changing the way we look at quality. To prove our commitment to quality, the company is investing in and prioritizing improvements for every vehicle that we build. As part of that commitment, we are also targeting existing vehicles on the road today and contacting our customers to provide these quality improvements, at no charge, that will help to improve your ownership satisfaction.
We are recommending the following improvements be performed on some 2005 through 2007 model year Dodge Charger, Magnum and Chrysler 300 equipped with a floor shifter.
The transmission gear shift lever interlock return spring hook on your vehicle may break. A broken interlock return spring hook will result in the inability to move the gear shift lever out of the "PARK" position.
What your dealer will do:
Chrysler will service your vehicle free of charge (parts and labor). To do this, your dealer will replace the transmission shifter interlock lever. The work will take about one hour to complete. We recommend that you make an appointment with your dealer to minimize your inconvenience
What you should do:
Simply contact your Chrysler, Jeep, or Dodge dealer, at your convenience, to schedule a service appointment. Your dealer will collect the necessary information to ensure that the appropriate parts are available so your service can be completed in a timely manner. Although not required, we recommend bringing this letter with you to your dealer, when you bring your vehicle in for this service.
If you need help:
Please contact the Chrysler Group Recall Assistance Center at 1-***-***-****.
If you would like to try the "over-ride" procedure, use the method below. If the over-ride does not work, this is confirmation of the broken spring, and the shifter will need to be serviced as stated in the Recall Letter above.
-Turn the key to the ACC or ON position.
-Remove the liner to the cubby bin to the right side of the shifter.
-Depress the BTSI override on the side of the shifter assembly.
-While the override is depressed, move the shifter out of the PARK position.
-Return the cubby bin liner to its original location.
If you found this answer helpful, please help me and leave a rating using the "stars" at the top of the page or click 'accept'.
If you cannot rate or do not see where to rate, please let me know!
If you have any further question, please ask!
Rating or accepting my answer does not cost you extra. It allows me to be credited for this Q&A.