Why will right rear window on a 2001 olds alero not go back up?

If you can hear the power window motor "trying" to work, and you still can't get the window to roll up, the most likely cause is a bad window regulator. In some vehicles, the regulators are made from plastic and become brittle over time. I had the same problem with a 2002 Jeep liberty and followed advice (see related links below for the reference) I found by googling on how the "repair/rig" the regulator to work again. As a worst case scenario, you may have to buy a replacement regulator. The good news is, it's not terribly difficult to replace, especially if your a do-it-yourself'er.