One other thing to try and cure the "not working at all" portion of your problem is to juggle the keys with the system on to see if that does anything.
Worn out ignition switches will often do just that - disable the climate control System. On second thought - In my car only the A/C was disabled, so that might not apply to your situation - Still, it is a simple test. Also, Also, regardless of whether "None of the fuses, including #5 are blown" I would still replace that #5 with a new one. Fuses are another mysterious thing with old MB's. They might look good - But looks are deceiving.
Hope this helps you some.