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There are several things that can cause your Cadillac Deville to have transmission problems. The most common transmission problems are worn transmission gears.
Absolutely
Can be the battery has a dead cell which will require the battery be replaced. Can also be anything on the vehicle that is on pulling from the battery. Any light that is on or any relay that is stuck will drain the battery. Check under hood light, trunk light, glovebox light, interior lights, etc.
dirt in the speed snsor bad speedo head in the dash
Heater coil
1 or more out of balance tires
A bad resistor or a bad switch.
One reason a 1998 Cadillac Deville would cut off while driving could be the fuel pump or the car is out of fuel. Another reason could be the spark plugs.
If the pedal is stuck down, no vacuum to the release diaphragm on the pedal
door button stuck --bulbs? fuse.
The blower control module is defective.
You may have an electrical short where there is a bare wire coming into contact with metal and draining your battery or you may simply have a light on that's making the battery's voltage to drop . An experienced mechanic will be able to conduct several diagnostic tests to determine the cause .