I have a 1996 Buick park avenue. The cooling fan contines to run even with the motor off. It runs until the battey is dead. What could be the problem? Thanks for any help.

Test or replace the Engine Coolant Temperature SWITCH. Also, test or replace the Radiator (Cooling) Fan Motor Relay.

Make certain that you're checking the correct switch: three wires are Yel, Lt Grn and Blk. It is mounted below the thermostat housing.
Be careful checking these circuits as the Powertrain Control Module (PCM) controls relay grounding.

If the switch and relays and harness are OK, your problem could be the PCM. Let me know.