Outside unit condenser fan not running. Compressor seems working OK.
I followed some advice to have run capacitor replaced but still the same. I also found there is a small noise inside the unit even we don't run that air conditioner. There is no sign we have a burned wire and fan motor likes fine.
The unit is a Trane XE 1000(TTR036C100A2).
I will appreciate it very much if any professional may provide some help.

Difficult to troubleshoot subtle noises from an AC unit from here.

A low hum or vibration may be the contactor coil or the control transformer.

The contactor (relay) for the fan may not be pulling in, or is pulling in an it has a bad contact that switches the fan on and off.

Really need a test meter to check these items out, not really a good thing to just try to guess which part is bad and just replace parts.

One test that you can make without the meter that tkrussell mentioned is to have the AC unit in the off position, you can probably do this by pulling the disconnect there by the unit. So with the power off take something long and slender and give the fan blade a turn and see if it turns easliy. If it does that should tell you that it is free. Then turn the power on and when you hear the units compressor running take the same thing you used before and give the fan blade another turn, if it tries to turn on it's on after you have ginen it a start that could mean the start capacitor. If it is hard to turn that means that you bearings are worn to the point that it is setting up a magnet and the motor will have to be replaced.