how to fix swamp cooler whose fan won't turn on
OK first thing I did was remove the motor and try it in a different unit.  It worked OK.  So the motor's not the culprit.  Another option would be to use a volt meter on the plug where it plugs in (turn the fan switch on first, check for A/C between basically all pins) see if it's passing current up there or not.  If yes, motor or connection to motor would be suspect.

Next thing was to test if the electric circuit breaker was working (either using a volt meter, or by swapping it with another one).  It was.

Next would have been to test the connections at the thermostat to see if they were "live" and if the thermostat, turned on, was sending "live" out up to the swamp cooler on the low or high wire.

But didn't have to, found my actual problem was that I was turning the fan to "low" but not adjusting the thermostat, which was still set to "very hot" so once I switched that, it all worked.  Go figure.