Dodge uses a plastic wiper bushing (ball and socket type) that connects the motor and linkages. It is designed to break before other more expensive parts, it can wear/dry out overtime. You can check by removing the wiper arms then cowl cover. You can check if it wore/popped off, it is loose, the part can be picked up from an auto parts store. I replaced one on an older dakota, the pack came with 2 was <$10. It is pressed into the linkage, can be difficult, but I was able to do it with channel lock pliers.
Auto zone rain x latitude will work pretty much the only ones that will
you havn't taken it to the mechanic yet.
Linkage bushings on wiper arms coming off back side of wiper motor under cowling
the wiper is held on by a nut where the arm pivots most likely the nut ont the non moving arm needs to be tightened there is a cap covering the nut remove the cap and tighten the nut when you have the arm in the proper posistion
well since the wiper do indeed work, i'd have to bet it's a fuse.
The linkage probably wore out and broke.
The 1999 Oldsmobile wiper switch can be located below the dashboard. The wiper relay switch simply plugs in and out.
If the wiper motor isn't working, check the fuse to start with, then the wiring connections. If the wiper motor is working but not the wiper arms, unscrew the cowl piece just behind the hood ( the part that looks like a grill ) and see if the little plastic inserts that hold the wiper arms in place have dry-rotted or not. They are available at your local dodge dealership and are pretty cheap.
Any other similar-vintage Mopar B-body (Dodge Coronet, Plymouth Satellite) should work.
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.
Either the wiper arm is stripped out or the linkage under the cowl panel has come undone.
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.