The linkage probably wore out and broke.
In many cars, there is only a single wiper motor. One wiper arm is attached directly to the wiper motor and the other through a linkage. If one is working, the motor is operating but the connection to the other may be broken.
Either the wiper arm is stripped out or the linkage under the cowl panel has come undone.
The non working wiper on the 2001 Century most likely has a broken wiper linkage. The linkage can be checked by removing the vehicles cowling.
Could be one of two things that I can think of. 1) the arm that comes of the the motor or 2) the splines on the wiper blade itself is stripped.
Its your linkage, not your motor.
Get a New one
Disconnected or broken control linkage? Bad wiper transmission?
It may be due to a broken linkage.
Wiper linkage broken or disconnected? Bad wiper transmission? Wiper Bushing. I have an '03. The wipers are crap! One goes out, once fixed-BAM...other one stops!!
If only one wiper is working then you have a linkage problem. There is an arm that runs from one side to the other. It has bushings that wear out. You can also have a stripped spline where the wiper arm hooks up.
You need to replace the wiper module. A few years ago GM issued a recall on these. Check with you local dealer to see if you car qualifies. If not it is an inexpensive and easy do it yourself fix.
A place where you can go to get a car's windshield wiper replaced is by either taking it to a mechanic or you can get the job done yourself. Just by simple buying a set of replacement wiper blades and removing the old ones.