If the fan in the air conditioner outdoor unit began to hum and not spin, the most likely cause is a bad starting capacitor, as in my case. I don't know why, the fan start capacitor usually fails before the compressor capacitor. When a capacitor fails, there is often no visible evidence of its appearance. You will need a capacitance multimeter to check this. This one is inexpensive. Before installation I measured the capacity. It was within spec. After I installed it, the air conditioning worked like clockwork. I hope this will take many years, but it has yet to be proven.