Airbag leak No air in suspension, back-end to the ground, gear shift locked up, safety mechanism i sopose.

Something wrong with the shift lock system maybe. Safety system that won't allow the gear selector to move from park unless the driver is pushing the brake pedal . Do your brake light's work ? Does your caddy have floor or column shift ?
Automatic Transmission Shift Lock Control Description and Operation (Floor Shift)
The automatic transmission shift lock control system is a safety device that prevents an inadvertent shift out of PARK when the engine is running. The driver must press the brake pedal before moving the shift lever out of the PARK position. The system consists of the following components:
• The automatic transmission shift lock solenoid (serviced as the automatic transmission shift lock actuator), as well as the body control module (BCM) and the engine control module (ECM).The shift lock solenoid is located within the floor shift control assembly with vehicles equipped with floor shift.
• The BCM controls the voltage supply circuit of the shift lock control solenoid. The following conditions must be before the BCM will supply voltage to the shift lock control solenoid.
The BCM controls the voltage to the shift lock control solenoid through the shift lock control solenoid controlled voltage circuit. The following conditions must be met before the BCM will supply voltage to the shift lock solenoid:
• The ignition is in the ON position.
• The ECM sends an input via GMLAN serial data to the BCM indicating the transmission is in the PARK position.
• The BCM determines the brake pedal is applied according the brake pedal position.
Since the shift lock control solenoid is permanently grounded, the BCM supplies voltage to the automatic transmission shift lock control solenoid, mechanically unlocking the shift lever allowing the driver to move the shift lever out of the PARK position as the solenoid energizes. When the brake pedal is not applied, the BCM turns the control voltage output of the shift lock control solenoid OFF, de-energizing the shift lock control solenoid. The de-energized solenoid mechanically locks the shift lever in the PARK position.
During remote start operation, the BCM will de-energize the shift lock control circuit, locking the shift lever in the PARK position.

I am mechanic I really need to no more make ect. but it could be battery or the ignition switch or ignition lock n key but like I said need more information this is a guess that I told you

AIRBAG PROBLEM MUST BE EITHER THE DRIVERS SIDE OR PASSENGER SIDE {IDE AIRBAGS}LOCATED AT THE SEATS.THEY TEND TO LOOSE CONTACT AT THE CONNECTOR UNDER THE SEAT.AS FOR THE SUSPENTION U NEED TO HAVE THE CAR DIAGNOSED FROM SOMEONE WITH A PROGRAMM AND EXPERIENCE.IS THE CAR LOWERED?IF SO AIR LEAK IS WHAT I CAN TELL U ROUGHLY!!!!

Most likely if its anything like the old lincolns the airbag/shocks are blown. If this is the original set on this vehicle very good possibility. Best fix is a replacement set or if the coil over option is available much sturdier.

In This car the leak is ALWAYS the airbag it self, and it is usually the front two that leak. Replacing them requires the front suspension be disassembled.

Check you rear air bag's, more then likely one has a leak.

Then noise you hear after shutting off the car very well might be the air suspension compressor. The air ride system is still activated for a half hour after the vehicle has been shut off. The roaring noise from the rear could be a bad bearing. The rear axle seals don't always leak when a bearing goes out. So it's not a conclusive indication that they are good just because the seals aren't leaking. If your mechanic isn't too versed in differentials it may be advisable to seek an opinion of a reputable transmission shop (however, that may be a difficult task).

Definitely sounds like there is a leak in your air suspension somewhere. I'd have a local shop check it out. There is a switch for the air suspension either underneath the glovebox right hand side of firewall. or in the back of the vehicle behind the left panel. it is labeled suspension

If you have a hole or crack in your airbag the compressor has to work extra hard to try to blow it up (like blowing up a balloon with a hole in it) I would recommend checking out strutmasters.com they have some great kits for the Ninety Eight. There kits will eliminate any problems with the suspension. It is a permanent fix. these convert you from the airbag to a powder coated American made steel coil spring that is guaranteed to last the life of the car. And for a very affordable cost. I added the link below so you can check it out.
http://www.strutmasters.com/oldsmobile-suspension-parts-s/85.htm

Hopefully this will help

Good Luck!!!

What has probably happened is you got a hole or cracks in your airbag. Dealerships and mechanics typically diagnoses it as the compressor but that is only to keep you coming back and wasting more money on something that will never truly be fixed. Both the airbag and the compressor are the problem. The compressor has to work extra hard because it is like blowing up a balloon with a hole in it. Therefor the airbag will kill the compressor. I would recommend going to strutmasters.com and taking a look at our conversion kits. these convert you from the airbag to a powder coated American made steel coil spring that is guaranteed to last the life of the car. This is a PERMANENT fix. I added the link below so you can check it out.

http://www.strutmasters.com/mercury-suspension-parts-s/25.htm

I hope I was of some help

Good Luck!!!