I also have an '89 LeBaron. My wipers did the same thing because the pivot bushings gave out. It's not hard to replace them, I pasted in below what I did to fix the problem from an earlier thread. Hope it helps.
The pivot bushings can be found on the Help! rack of any parts store. All the post 1979 Mopars seem to use the same bushings.
1) Remove both windshield wipers from their pivots. Use a flat blade screwdriver to release the little slider that locks the wipers down before removing.
2) Remove the plastic cowl cover. Do not remove the hood to cowl weatherstrip. It's not necessary. Oops. rolleyes.gif
3) Remove the plastic wiper motor cover and the plastic grate pieces just below the windshield wiper pivots.
4) Remove the 10mm windshield wiper pivot mounting bolts from both the driver and passenger side wipers.
5) Remove the three 13mm wiper motor nuts. If you haven't done so already unplug the wiper motor harness.
6) Lift the wiper motor free from it mounting bolts. Once the motor is free, you can slide out the whole wiper arm assembly along with the linkage.
7) Since I had already lost the passenger side bushing, I used a combination of a large washer, a deep socket and a pair of channel lock pliers to press the bushing into the wiper linkage. I put a tiny dab of grease inside the bushing and used a washer to protect the upper surface of the bushing to press the wiper pivot in place at the bottom of the bushing.
8) Cut the other bushings off with a sharp knife, and repeat step 7.
9) Feed the wiper linkage through the firewall hole and put the wiper motor back onto the mounting bolts. You can use the holes where the plastic grates were removed to get hold of the pivots and swing them back in place.
10) Use at least one bolt to tack the pivot back in place. Do the same thing on the other side. Then put in the rest of the bolts and put the retaining nuts back on the wiper motor and plug the harness back in.
11) While the cowl cover is off, activate your wipers and watch for operation. Everything should be smooth and quiet with no binding.
12) If you havent' done it already, now is a good time to remove leaves or other debris out of the cowl.
13) Put the wiper motor cover back on and replace the plastic grates to keep debris out.
14) Put plastic cover back on. If the plastic retainers are trashed, replacements are easily available from the Help! section of any auto parts store.
15) Replace windshield wipers on pivots. You should be good to go!
This post has been edited by patricklynch: 19 August 2008 - 06:38 PM