As far as I've seen, the most common problem with the controller of the a/c and the like, is the circuit boards getting old and solderjoints cracking. If you search this site with that in mind, you should be able to find alot of usefull info. If you want my own personal opinion, I would suggest taking out the circuit behind the buttons you see (I'm not sure of the least distructive way of doing that) Once it's out, use a medium-wattage, around 45ish, and re-flow every solder joint on the bottom and top boards. If it's done right, this technique can fix many problems with the a/c. I've done the same thing with my idle speed controller two days ago and it fixed my idle problem right up.

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iThink Different
Building an all new electrical system in my
1985 500SEL