Why does my car keep getting stuck in park?

That would be called the shift interlock feature. It operates on the same circuit as the brake lights so the first thing you want to do is to make sure the brake lights are working when this problem is present. If the brake lights are working, that proves the circuit is good up to that point, then you'll have to get to the solenoid in the console. Disassemble as much as you have to to access the solenoid near the shifting mechanism. Us a 12v test light to test for power coming and going at the solenoid when the brake is applied. If power is arriving and switching and the solenoid is not triggering, the solenoid is bad and will have to be replaced.