Take your door panel off and replace them...
The way that replace a window regulator in a 2003 Buick LeSabre front drive side is by removing the door panel. Next, disconnect the electrical connector on the regulator and replace.
Yes
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Most likely it is the regulator, either the cable is broken or the plastic at the top broke and the cable became unspooled and wrapped around itself. The window is held in by two screws that tighten a clamp on the window that holds pretty tight so it is doubtful it is that.
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See this post for instructions and photoshttp://www.ricksfreeautorepairadvice.com/repair-topics/window-power-repair/replace-a-power-window-regulator
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How much can cost repair to change head gasket Buick Rendezvous 2002
replace 2002 buick rendevous motor mount
Replace window regulator.