start by removing your wiper module, which is located near the wiper motor, open it and spray with contact cleaner...
if the problem still exist bring your wiper module to your trusted electronic shop, so they can check if there are components which are cut or rusted.. so they can clean it properly and attach components.
by putting on a new one
first have wiper swith checked to make sure it is not the problem then have wiper motor checked for a short a short inside the motor will keep it running
Broken linkage? Disconeccted linkage? EDIT::: The most likely cause is a bad wiper control module, its attached to the wiper motor
about 200 quid
Replacing a wiper motor on a 2004 Chevy Impala can be difficult. It is best to take it to an auto repair mechanic or an authorized Chevrolet dealership.
if the shaft of wiper motor is moving you probably have stripped gears in wiper arm or the nut to hold wiper arm in place is loose
You have to diagnose it first. With key on and wiper switch on, listen carefully, if you do not hear an electric motor running check the fuse. If the fuse is good and the wiper motor is receiving power and ground, the wiper motor assembly is probably bad. If you hear a motor running but nothing is moving, the wiper transmission assembly is stripped or the linkage is loose and came apart.
bad wiper switch Or, if you are certain the motor is running, the linkage could have become disconnected.
Windshield wiper motors have an internal switch that allows a wiper motor to stay running long enough to keep the wipers moving until they reach the "park" position. Once the wiper gets to the park position, the wiper motor is shut off. The internal switch often fails and either the motor will shut off immediately, wherever it is or it will keep running. It sure seems that you need a new wiper motor.
Remove the wiper arm from the wiper motor. Remove the wiring harness from the wiper motor. Remove the wiper motor retaining bolts. Reverse the process to install the new wiper motor.
Remove the wiring harness from the wiper motor. Remove the windshield wiper arm from the wiper motor. Remove the wiper motor retaining screws. Reverse the process to install the new wiper motor.
Wiper arm travel rod from the wiper motor. Remove the wiper motor wiring harness. Remove the wiper motor retaining bolts. Reverse the process to install the new wiper motor.