Can't get 1995 buick century out of park

Sounds like the Interlock switch is not connecting with the brake switch.
Your car is built to prevent shifting out of Park unless the foot is on the brake pedal.

You can probably verify this problem by stepping on the brake pedal and observing if the brake lights come on. If the brake lights do not work, then the switch on the brake pedal lever under the dash is broken or misaligned.

This is a more common problem than shift cable failures, but you can't ignor that the shift cable may not be moving due to a broken cable. Either problem is not very expensive to fix, but will complwtely immobilize your car.

It is not impossible for the Transmission to jam or the Park detent to break, but it is an opportunity for dishonest people to sell you a new trans for the sake of a simple switch. So If a trans is indicated, get a second opinion.

This car has a park lock safety system that is released by the application of the brake pedal, so the first thing to do is verify the battery is good, if that is ok then check the brake lights, they must work to release park.