Carrier AC Compressor and Fan not starting

Hi All,

I have a Carrier 38CK-036-340 AC from 2001. A month or so ago I uncovered it and ran it for about 15 minutes with no issues, the temp then was in the upper 70's.

Yesterday we had the first day just short of 90 and today and tomorrow are expected to be over 100.

I turned the AC on yesterday and the in house fan started running but the compressor outside never started. I could hear a humming sound so I immediately turned things back off.

I took the cover off and the contactor is closing, that was most of the humming sound, but neither the fan or the compressor are starting. There is no dirt built up, fan turns freely. There is no obvious leakage from the capacitor.

My question is whether a bad contactor or capacitor, or even a bad compressor would also keep the fan from starting?

Given the costs I am thinking of ordering the contactor and capacitor and just replacing both.

Any insight appreciated.

Thanks,

Jon