If you're experienced enough to work on electrical equipment safely while it's energized, you can measure the voltage between the common and "run" connections to the compressor, and separately the common and "start" connection, while the unit is starting. Be careful since the start voltage can be well over 200 VAC due to the inductive effects of the starting coil. It is also useful to measure the current in these circuits.
If the voltages look OK but there's no current in one or the other then the compressor is shot. Not unusual for them to go bad after that many years, usually due to cumulative and progressive breakdown of the stator insulation.
A 1993 unit is new enough to be a standard 14" square opening, so I would just replace the whole thing if the compressor is shot.
To learn to see below the surface, you must adjust your altitude