Constant Alarm Tone

I recently purchased a 1991 Lincoln Mark VII LSC 5 Litre V8 Automatic :( with 72,000 miles. Runs fine. When first started after a while a beeping alarm sounded every second (beep beep beep beep)and would not stop until I pressed the clock button on the panel of computer buttons (Clock, MPG, Elapsed time, etc, ). Recently, after driving for a minute or two, the beep comes back but instead of an intermittent beep beep beep, it is a steady unstoping tone that will not stop unless I turn off the ingition. If I open the door, the tone stops and I hear the door ajar alarm instead. No dummy lignts or other warnings come on while the tone is going off. It is loud enough to drive someone crazy on a long drive. Any clues on how to repair the malfunctioning alarm (tone) or stop the tone altogether?