This is a fault in the shift interlock system which is a safety device which prevents the shifter from being released without the key on, and brakes deperessed. It can very well be as simple as a faulty brake switch mounted above the brake pedal. Have an assistant monitor the brakes lamps to see if they illumnate when you step on the brake pedal.
No need to replace any component yet. The brake light illumination entails the power is most likely getting to the shift lock in the steering column. Now, can you hear a clicking in the column with the key ON, while stepping on the brake pedal repeatedly? Also, try to push the shift lever further into park and hold it firmly, while stepping on the brake pedal, repeatedly. If the shift lever releases, than the shift lock soilinoid is most likely at fault. Also, try turning the steering wheel back and forth, with the ignition key ON, and stepping on the brake pedal. Let me know your outcome.
Alright, it does seem the problem will lie in the steering column, shift-lock assembly. One other test you can make if you feel comfortable doing so, is disconnect the transmission shift cable underneath the vehicle at the transmisison. Be sure the wheels are chocked so that you do not mistakenly have it out-of gear. If the shift cable is removed and the shifter comes out of park, the problem lies with a bad cable or inside the transmission "parking prawl." But in most cases we have a locked up shift cable or shifter inside the column. Both require some exoperience to replace and I would recomment be done at a facility equipped to do so.