New to the forum so hi. I have a 2006 mini base. AC has been working great. Got off work and no AC. I also only have high speed radiator fan operating. I’m trying to see if someone knows that if the low speed fan not coming on would that keep the compressor from coming on and running? Any help appreciated. I replaced the rad cooling fan about a year ago

I believe so, my ac clutch would kick on for like 2 seconds then off. My ac was blowing hot. My high speed fan only was working. Replace my fan and ac works fine now. Also would get hot in traffic. Best bet replace fan assembly.

Test your fan resistor first....I bet that's your fan issue......if the fan does not work, it won't draw cool air through the front of the car and keep the condenser cool.....which could result in high AC pressures and if the pressure gets too high, it will dump AC refrigerant out the blow off valve

So the story goes, and what I believe happened to me: Low speed fan goes out, all is fine until AC compressor overheats and dies. My solution was to replace the fan/resistor, and AC compressor.

from a long ago post:
Per the Bentley manual, and confirmed by my ScanGauge, the fan operates at low speed at 221F, and turns off at 214F. The fan switches to high speed at 234F and remains on high until the coolant temps drops by 7F. Supposedly it also turns on when the AC is on and the AC system pressure reaches 8 bar (114psi)

*In my case the AC compressor died, so even after a new fan, the low speed didn't come on with the AC, as apparently the compressor wasn't developing 114psi
After I installed a new compressor, the low speed fan functioned as designed.