I would never use a 3 n 1 RCO410, they have caused fires in the past. I would first check for burnt wires to it, or burnt compressor terminals. If you have a meter, verify you get 115 volts to the compressor while it is plugged in.
If you have a mechanical coil type relay, these rarely fail. If you have a meter, turn it upside down and check continuity between the input spade terminal and the round right compressor terminal. If shorted, the relay is ok, your compressor run winding may not be drawing enough current to activate it, most probably from burnt wires.
If it still will not work, you can try a AP4503418 start device. Does not come with instructions, but you just plug it in the compressor and insert the fridg wires into it.