if you can hear the motor turning when it's trying to go up, I'd bet on a mechanical issue. Pull the skin off the door and investigate further.
If you can't hear anything when the window is being sent up, and it works from the driver's door like you said... definitely the rear door switch or the wiring going to it, try flipping the switch around 180 degrees and plugging it back in. If the window will now go up but won't go down, replace it and you're good to go, else you have wiring issues to track down.
The way the door switches work is an On-Momentary-On DPDT toggle switch being used as a polarity reverser - pretty much it just applies power one way to go up and the other way to go down.