It can be a bad compressor if it will not start also!!
Ok we do not need to test for voltage be cause we know it is getting voltage by it`s buzzing and pop!
So you will need to turn the unit off By unplugging it at the outlet or turning the breaker OFF .
Note: just turning it off on the controls is NOT enough!1
With it unplugged remove the relay and overload off of the compressor and you will need to ohm out the three terminal winding lugs to each other looking for resistance on each to each other.
no specific value just resistance .
If the compressor does have resistance we can assume it is good .
But that may not be correct.
If the windings show resistance it can still be locked up / stuck internally and the compressor would need to be replaced.
A service technician would test the compressor amperage draw (amount of amperage it is pulling when trying to start to be ale to tell if the compressor was good or not ,
But most home owners do not have a Amperage meter to be able to test this.
So if the windings do have resistance the only thing we can do is replace the relay and overload and the see if the compressor will start.
The two (overload and start relay ) would cost approx $50.00 to test and see if it will then start and run.
Let me know what you find and if you need part numbers I can also give you that.