One or more of the power window regulators (one in each door) may fail causing the window to fall into the door and not roll up.Google+
Car Problem Reports
Cadillac DTS Power window regulators may fail and cause window to fall into door
Cadillac DTS Problem
Model Year Affected: 2006
Visitor, 2006 Cadillac DTS, 118,000 mi
Opened rear passenger window half way and would not go back up. Could hear the motor running but window would not move. Had to replace the window regulator. Have not had any additional problems with other windows as of yet.