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.