The first three things to check are
- Window Switch
- Wiring harness where it goes into the door near the hinge.
- Window motor assembly.
It's easiest to do this with a voltmeter (DC Volts function on a digital multimeter, 0-20 V range). Remove the trim panel from the door and inspect the window mechanism to be sure the actuator arm is in place.
If the wiring goes directly from the switch to the motor, that makes
identifying terminals easy, and possibility 2. is eliminated since the other windows are known to work through the switch assembly on the door. If the wiring goes out of the door and back in to the motor, see if you can match wire colors
at the switch with those on the motor. Turn on accessory power and check for voltage on the motor terminals (connect the meter's COM lead to the motor ground and measure with the V-Ohm lead). You should measure 12 - 13 Volts on one of the motor terminals when you hold the switch in the down position.
If you do not find voltage on any terminal, the problem is 1. or 2. above. Find the power feed to the switch assembly (probably the heaviest wire going to the switch). (If necessary, post back and I will check the library to find out what the wire colors are - I don't have access to it at this time.) Turn off power, switch your meter to the Ohms function (lowest range), and connect the leads between the power feed and the down switch terminal. Hold the down switch on (you may need a helper to give you the third hand). You should read no more than a small fraction of an ohm resistance - close to what you get when you touch the two meter leads together. If this is not the case, the switch is bad. It is possible to pick the switch assembly apart and clean the contacts, but it is a delicate job - the snap-together tabs break very easily, and you have to keep track of the parts for all of the switches.
If you get voltage at the motor, but do not hear the motor running, the motor is either locked up or the thermal protector is burned out. If you hear the motor running, but see no movement, the window transmission is jammed or stripped. If you see the window actuator arm moving a bit, then stopping, the window is stuck. The GM electric window drives I'm familiar with are permanently crimped together and are not designed to be repairable. If the problem is inside the motor and gear assembly, that would have to be replaced as a unit.
