Fan would not work and it was 9 years old. Thought it was time so I replaced the fan and capacitor but still have the humming noise. Fan will still not kick on. Blows cool but not cold inside. Any suggestions?

Is this the fan in the inside unit or outside unit? Exact brand and model number of unit causing problems?

Outside unit. It is a carrier model number 38ckc060310 9

Check the contactor in the outside unit and see if it is pulled in when calling for cooling. It should pull in on a call for cooling and drop out when the call for cooling is over. Post back with results of what you find.