Shifter is stuck in park and car says it's in neutral

You can try a self-diagnostic test. To activate self diagnostic program:

With the ignition switch in the OFF position, depress the TRIP and RESET buttons.
While holding the TRIP and RESET button turn the ignition switch to the ON position.
Continue to hold the TRIP and RESET buttons until the word CODE appears in the odometer windows (about five seconds ) then release the buttons. If a problem exists, the system will display Diagnostic Trouble Codes (DTC's). If no problem exists, the code 999 (End Test) will momentarily appear. You may get a P0928 code, it's the bsti, or Brake transmission saftey interlock.
Theory of Operation The Brake Transmission Safety Interlock (BTSI) is a safety feature that prohibits movement of the shift lever out of park unless certain conditions are met. The Cluster controls the BTSI solenoid. The Cluster will engage the BTSI solenoid when the module detects the depression of the brake pedal thus allowing the transmission shift lever to move from the park position to any other position. Failure of the control circuit may inhibit the movement of the shift lever and cause this DTC to set. When Monitored: When the ignition is in accessory, run or start position. Set Condition: This DTC will set if the Cluster detects a problem with the BTSI solenoid control circuit. The DTC will remain active until the Cluster no longer detects a failure of the BTSI control circuit.

Will send testing info by email.

That recall had nothing to do with this. This may sound like a stupid question, but are the brake lights working when you hit the brakes?

Inspect and test the brake switch if okay-check the shift interlock control system

Found this you may want to try.
The gear shift in the automatic transmissions have a spring that allows you to take the vehicle out of park that is connected to a pink piece next to the shifter on the drivers/left side. The pink piece is prone to failure and breaks thus releasing the spring.

The correct fix to this is buying the $127 transmission shifter assembly. There are methods to allow you to drive it to the dealership. One way is to remove the chrome bezel around the shifter, on the center console, and use a screwdriver to pull the pink piece located on the left of the shifter towards the back of the vehicle after applying sufficient pressure to the brake pedal. This will allow you to make it to the dealership to buy the part to fix it or allow them to install it for you.
Or
Sense you now know whats wrong with it you can quickly repair this your self and save the $127. Pop out the A/C control panel it has 3 plugs on the back of it and 1 plug for the middle console, next remove the 2 10mm screws located near the top where the A/C panel was and the 4 in the middle console. Pull up on the emergency break hard so that it is all the way out of the way. At last lift up on the middle console and it comes right out. The FIX is simple and better then the factory replacement part, drilling a small hole through the pink plastic about 2 10ths of an inch away from the right side. Reattach the spring to the new hole and the black tab on the right back side it's about 2 inches from the pink plastic. Then reinstall everything. Hope this helps, and saves you some money.

Check the brake lights. If they are not working, the interlock system would prevent you from shifting out of park.

The cable is either broken or it's disconnected on one end.