You might also think about the ignition switch. The contacts can arc and overheat, and the terminals in the connector can get hot enough to melt it. That was a common problem on '95 and older models, especially for people who used the heater on the highest speed a lot. I can't remember if that applies to a '96 because they do the fan speed switching with a ridiculously unreliable computer module and that high current wouldn't go through the ignition switch then.
The rear wiper controls are built into that heater control module too. It's on the back of the bezel around the radio. Since that computer switches a high current on and off, I suppose it too could develop overheated connector terminals but I never ran into that myself.
One thing to be aware of is you may need to reprogram that computer if you unplug it to look at the connectors. For the '97 models that can be a real frustrating task. By 2000 or 2001 they did away with that. I can't remember ever doing the procedure on a '96 but if it's the same as a '97, it will not pass one of the self-tests if the air conditioning isn't working.
If the six yellow leds in the wiper and washer switches are blinking when you're done, here's the procedure to reprogram the computer.
http://randysrepairshop.net/reprogramming-the-chrysler-hvac-computer.html
You can also have a worn fan motor. When the brushes wear down they make intermittent contact with the armature. Usually they fail to start up until you hit a bump in the road. If the motor quits while driving after it has been working, a more likely suspect is a poor connection in an electrical connector, or a problem in the heater computer.
Friday, October 5th, 2012 AT 3:35 AM