Back Driver's Side Window

Before anything else, what's the position of the window lockout switch on the driver's door switch panel?

 

Have you tried using both the driver's master control mechanism and the window switch which is at the offending door? Sometimes the switch goes bad.

 

sounds like the door lock mechanism is jammed in the window gears

 

If you press your ear against that door while pressing the "down" switch do you hear any motor like sounds? If so it is probably not electrical but mechanical. That includes possibly a bad or weak motor, but not "no signal to motor". If you hear nothing at all then electrical issues of the "no signal to door" type move to the top of the list. There is some overlap, a bad motor might or might not make a sound.

Sometimes a really dirty window can stick so tightly to the rubber at the top that the motor cannot dislodge it. Since you just bought this used perhaps it was sitting around unwashed for an extended time, which can lead to this issue. To fix that problem first wash the top of the outside of the window glass at the rubber seal with water from a squirt bottle. Then dry the glass. Then with the door open put a hand on each side of the window (like you are pressing your hands together) and pull down gently while the switch is activated. If you don't have a friend to help that can be done with a toe, but it sure looks peculiar to onlookers. Once unstuck such a window will move normally up and down, so let go as soon as it moves. If that works clean off the rubber with a damp cloth, and also the top of the glass, so it won't stick again.