it sounds like your neutral safety switch
Because its a 1988 Buick LeSabre
what can cause a 2002 buick lesabre to not crank
Illustrate how to jump start a 2004 buick lesabre
If you lights do not dim when turning key, then probably your starter.
Check to see if the brake lights are working - shift interlock and stop lights are on the same circuit - check the fuses - Try turning the key to the 1st (unlock) position shift to neutral to start and then shift to Drive Check the shifter interlock switch on the brake pedal. Possible linkage problems also.
car stalls backfires hard to start
the contact wires under the driver side airbag may be stuck
check igntion coils
fuel pressure injector pulse idle air control motor
Bad key or ignition switch
Cheap gas, try putting the highest octane, believe me it will make a difference.
The switch is on the steering column about 18 inches from the floor and held in with 2 screws,. Put a new one in then adjust it by moving it back and forth to where it will start and turn off in the proper position.