I have a similar problem on a 92 LeSabre, which I have yet to fix, since my daughter drives the car. In the short term we found that releasing and stepping on brake pedal several times may do the trick in the short term.
From looking in a few manuals as well as a brief discussion with a couple of repair shops I called for estimates, it could be a problem with the switch at the brake pedal either being improperly adjusted or a switch failure, or a problem with the shift interlock solenoid in the steering column. This switch powers a solenoid in the column to allow the shift lever to be moved out of park. It appears from schematics that one could test the solenoid by hooking a +12 V jumper (a long piece of wire from your local hardware hooked to the +terminal on your battery) directly to the dark green/white striped lead off the brake switch (the one switch that does not have the large vacuum hose to it, but does have a total of six wires associated with it). If, when the jumper is hooked up, and the ignition is turned to on, one can shift out of park, then the solenoid should be working 'Ok' and either the switch needs adjustment or replacement. Adjustment instructions can be found on various web sites or in a Chiltons manual at your local library, although it looks like one simply pushes the switch in as far as possible, then pulls up on the brake pedal until it stops moving or the switch stops clicking, and the brake lights stay off when the brake pedal is released. Also check that the brake lights go on when the pedal is depressed.
Estimates for repair ranged from about $30 for a switch related problem to about $150 if the solenoid needed repair (about $70 labor and about $70 for a replacement solenoid). So it can't be too hard to take the solenoid out and repair/replace the solenoid as $70 labor is only an hour or so of labor costs. Again, instructions can be found in various places on the web.
If you want to try it yourself, you need to remove the lower plastic shield on the dash, just above the pedals. The solenoid itself isn't in the steering column, but visible from under the dash on the left side (drivers left)between the column and the parking brake. It has a bright grey, almost galvanized finish on it. If you put the keys in, and turn the ignition to "on", then push on the brake pedal, you should be able to see the linkage move and hear the solenoid. The moving part of the linkage is mounted to the solenoid bracket with a 10 mm nut. You can also turn the ignition key to "on", then manually move the linkage at the solenoid to see if the shifter releases. The solenoid has a resistance of about 14 ohms when measured with an ohmmeter. You can use a jumper as mentioned above to put +12 Volts on the solenoid by running a wire from the upper (or "electrically hot") part of fuse 15 (which is the courtesy lights fuse)to the dark-green with a white stripe wire on the 4 wire connector that goes to the brake switch that does not have the vacuum hose on it. When 12 volts are applied you should be able to see the solenoid move and hear it too. The shifter won't release unless the ignition key is also in the "on" position.
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