I have a 2 ton century A/C unit. The outside unit will not come on, but it hums. I have determined the following:

The air handler fan in the inside unit comes on.
The compressor and the fan in the outdoor unit do not come on, but it hums. (I assume the compressor is not coming on... lines are not cold)
The contactor is working (the contacts connect when energized)
The dual run capacitor reads open (infinity) on both sides and it doesn't read any voltage after I check it with an Ohm meter, then put it on A/C volts.
I read 2.2 ohms across the compressor leads (red and blue)
I read 83 ohms across the 2 fan motor leads (yellow and brown)

According to the readings, I think I have a bad capacitor. Would that be correct?

Thanks for any help!!

Sounds like a shot capacitor. I had two blow on me in the past 5 years, and both times it acted as you describe - a loud humming but the compressor fan wouldn't come on.

Do you have voltage to the contactor on the air conditioner?