If you are using a 3n1 relay and you have power to the relay and the compressor is not running you have a bad compressor.
Take a VOM set to OHMs and read the 3 compressor pins to ground( a refrigerat line will do).If you get a reading the compressor is bad. If not,
Read each pin to the other pin, C to S, C to R, S to R.
C to S and C to R should total the S to R reading.
If that happens you have other issues.
Do these steps and report back.
If I am not online someone else will give you the next step.
In case anyone is interested :
Single phase compressor motors have a "Start Winding" and a "Run Winding" with a "Common" connection between them. Therefore the total resistance is the sum of both windings.
Shorted motor windings:occur when the insulation on the windings become defective and allows a shorted condition (two wires to touch), allowing a bypass of the winding. Depending on how bad of a short it is possible for the compressor to operate, but will draw excessive amps.
There should be no reading from any terminal to the compressor motor case using an ohmmeter.
Grounded motor windings occur when the insulation on the winding is broken down and becomes shorted to the compressor motor case.
This can be verified with an ohmmeter by touching one lead to any terminal to the compressor motor case (it is recommended to scrape away paint).
A compressor motor may have a weakened winding that will short to ground when called to run. It is therefore recommended that a "Hi-Pot" tester be used in conjunction with an ohmmeter to check for insulation failure.