Peter:
Pumping the compressor down can do a compressor valve check. If it will not pump down, or pumps down slowly, one or more suction valves may be bad.
If the compressor pumps down and off but the pressure on the suction side rises rapidly, one or more discharge valves are bad, the pressure relief valve is leaking, or you have a blown gasket. If the compressor is going off on the oil pressure control you may have a broken oil pump shaft or an oil pressure-regulating valve that is stuck. Most low oil pressure problems are a result of worn bearings causing a loss in pressure around the bearing surfaces.

Other causes for low oil pressure are high temperature and oil dilution. A broken oil pump shaft results in zero or no oil pressure and maybe a result of a bearing failure allowing the compressor crankshaft to bounce and snap the oil pump shaft.
I believe most technicians agree that replacement compressors fail at a rate several times higher than original equipment compressors. It is the service technician's responsibility to determine not only the reason the unit isn't cooling, "compressor is shorted to ground", but also what caused it to fail and to correct any system faults. Keep in mind that few compressors you replace actually ware out due to age. When you're called
To fix a system with a bad compressor, try to remember that the bad compressor is most likely a result.

Some of us have seen compressors that have been running for thirty or forty years but most of what we change have less than ten years running time. Most failures fall into just a few categories such as the loss of lubrication, which is probably number one and many things can cause this, but most are system faults rather than compressor defects. Any system fault will eventually show up in the compressor.
Roger