There are several things that could be preventing the compressor from being actuated by the climate control amp, including sensors, cutout control unit, or the climate control unit itself. I agree with the previous suggestion in this case, get the CD and work through the control problem. Hopefully you won't have to replace the evaporator, good luck in finding the leak.
I thank my lucky stars every time I get in my 300E and the A/C works one more time. I have a nightmare that the same problems that you are dealing with will show up on mine.
I will be in Stuttgart Sunday and Monday. While I'm at the MB Museum, I'll see if I can find the alter where I can offer a prayer to the Benz gods for you.
Best of luck with it,
'84 Euro 240D, 523K miles
'88 300E 5 Speed
'81 300D Daughter's Car
Over 800,000 miles in