Turn on the AC at the thermostat, and the fan on the house'* AC condenser unit outside doesn't turn...but the motor hums and gets hot. Compressor does kick on.

If I shove the fan blade with a stick, it does turn and stay turning full speed.

According to my brief research, this points to a bad fan start-up capacitor. I have located the cap, and it doesn't look bad (no bulging, corroded contacts, etc.), but what do I know.

So, rather than throw parts at it or (egad!) call in a service guy (unit'* long past warranty stage), how do I (safely ) test the capacitor?

I would say for as cheap as the CAP would be you dont bother just change it.