I have a 2006 suzuki forenza and this happened to me. I talked to the mechanic at the dealership and he said it was the brake light switch and that it was a safety feature so we would not drive the car with no break lights . I ordered one from them and just paid for the part. my husband was deployed so I looked up "how to change the brake light switch online (and I know absolutely nothing about cars). and it was pretty easy. Once I changed it out, it shifted out of park with no problem.
Check to see if your brake lights work. If the brake light switch fails it is a key input to the shift lock control that prevents the transmission from coming out of park. On a lot of cars you can hear a clicking sound around the shift lever area when you press the brake pedal with the key on. One of the wires at the brake light switch should have power key on or a fuse or wiring issue is the problem, on pressing the brake pedal that power should be transferred to the other side of the brake light switch.