I believe the question was about testing compressors and not test cords. Now to test a compressor fully you should not only take in to account the electric motor but its mechanical components as well.
Starting with the electric troubleshooting.
A compressor ( and I mean the motor) can fail and have either open windings or shorted windings, note that the windings can be shorted among themselves or to ground, chassis or the case (it is all the same thing).
Open winding means the compressor wont run and probably trip the overload protection, a shorted winding will either activate the overload or blow a fuse (depending how solid is the short)
Now an open winding is always conclusive test but to distinctively conclude that a winding is not shorted is difficult because motor windings have a very low resistance. You will require a good deal of judgment (experience) and a very precise instrument to test compressors in this fashion. One exception to above is a winding shorted to ground, this is always conclusive when it shows up, however even these failure modes are not detectable all the times and for this reason many professionals use insulation testers to uncover them. At this point it is a good idea to use a test cord and see if the compressor operates. Note that with use and age compressors can require more starting torque to turn and may require a starting capacitor or hard start to get it rolling.
If your compressor still refuses to run the problem is in the overload or mechanical in nature, if you believe the problem to be mechanical let us know.
Now after five hours of reading over Copeland Application Engineering Manuals as well as their and Tecumseh Service Data Guide this is what I have come up with, again let me state the information below is from them not I.
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.