This is not a do-it-yourself repair. You can pull the door panel off and peek inside, but be warned, the mechanism consists of cables, pulleys, and a spring-metal band wound up in the motor. I never actually worked on one of these nightmares myself, but it wasn't hard to hear my coworker's comments as they ran all over the shop chasing that spring! Lots of frustration from what I understand.
I also can't tell you what to look for, but if you're mechanically inclined, you should be able to figure out if it's a broken cable, or pulley, or the clip that attaches to the window.
Since you were able to pull it up and tape it in place, I assume it's a mechanical problem, and that you can hear the motor run. If you can't hear the motor, the most common cause is broken wires between the door hinges. In that case, the passenger window won't work either from the driver's door, but it will work from the passenger's switch.