I have never seen a flat cap.
Are you sure what you describe is not a PTC
(Positive Temperature Coefficient Thermistor) serving as a start relay?
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As for testing a cap, check resistance with multimeter.
It should begin low, and slowly climb to infinity; but this is
not definitive because multi meters use a DC Voltage far
below the cap's rating.
The relay is far more likely to fail.
To begin, unplug the machine until the compressor
is cool. Observe compressor closely when plugging
the machine in. If it restarts, it was overheated and
requires condenser fan service and or condenser
cleaning. If the compressor does not start but makes
a single click after about 5 seconds, the thermal protector is good. To check the relay and cap, identify: start, run, and common terminals on
the compressor. Remove original wiring. Using a plug and cord with bare ends attach a neutral to start and run. Using caution, touch line to the common terminal. Whether the compressor starts or not discontinue power after 2 seconds at most.
If the compressor does not start it will not.
If it does start, replace the cap, relay, and thermal
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