Your 1979 450SL has the very troublesome climate control II system. To verify this, take note of the fact that you have buttons vertically oriented, and a separate AC rocker switch to the right side of the vertical row of buttons. This system depends on NO vacuum leaks anywhere in the vacuum pods, as a single leak will lower the vacuum and prevent the vacuum switch that should turn on the compressor from operating. Try pushing the defrost button in and turn the AC switch on, this bypasses some of the vacuum stuff. If your compressor will rotate in this configuration you have vacuum leak problems. To properly troubleshoot this setup you will need the vacuum diagrams. Also, the engine must be running so as to provide vacuum to the climate control unit. Does your servo operate correctly? It is the black unit under the hood on the right side close to the firewall. Usually they are rusted up inside and do not work. I ended up purchasing the digital servo for my car, it works great! (I also have a 1979 450SL and have been through this exercise myself.)

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Richard Wooldridge
'01 ML320
'82 300D 4.3L V6/T700R4 conversion
'82 380SL, '86 560SL engine/trans. installed
'79 450SL, digital servo update
'75 280C