Why are my headlights and wipers not working on 2002 Jeep liberty sport 4x4?

Could be the speed sensor has loose wiring. Speed sensor is usually located on the end of the transmission housing. Here is a link to the same problem by another person and a possible solution.
https://answers.yahoo.com/question/index?qid=20081103061522AAGxZYf

check your wheel speed sensores

If the speedometer does not work but the odometer does, the problem is in the speedo cluster. If neither work, it may be the speed sensor on the side of the transmission.

The routing of the speed sensor wires is located on the rear differential. The problem is that they rub on the E-brake cable and once the wire is exposed they short and the speedometer and any other options running off the speed sensor quit working and that includes the transmission shift points and can cause the torque converter to not unlock and cause stalls. We went to a dealer and got the replacement kit for $32.00. He also took the time to encase the wires in a plastic tubing to avoid this problem again.
From forums.cnet.com
http://forums.cnet.com/7723-7811_102-261115/jeep-liberty-2002-speedometer-not-working/

Hi

Check if there fuses related to the speed sensor or speedometer. there could an expose cable that might have triggered the speedometer to work.

Koxo

Speedometer cable may have broken. You can't tell from the outside of the cable, since it has a plastic shield. You have to disconnect it from the transmission to check it. If you can turn the cable inside the shield easily, it is broken.

Are you looking for a certain sensor? What engine?

check fuse in fire wall open the hood of your jp or by your gas and break pedal

Jeep Liberty 2002 woahs !
by porth21 - 2/1/09 7:35 AM In reply to: Jeep Liberty 2002 speedometer not working by Dannywon
I have a 2002 Jeep Liberty Limited with the same problem. The main problem I have found to be the routing of the speed sensor wires located on the rear difrential. They are 2 blue wires on my jeep and probably the same on yours. The problem is that they rub on the E-brake cable and once the wire is exposed they short and the speedometer and any other options running off they speed sensor quit working and that includes the tranny shift points and can cause the torque converter to not unlock and cause stalls. I am having the same problem for the third time and chrysler and jeep are both aware of the problem and unwilling to repair the problem or post a recall.