This might well be a ridiculously easy question, but please keep in mind I have essentially no idea what goes on inside an electric motor. My sparky handled the brain work; I ran cable and did very simple installations.
I have a residential-quality fan on a floor stand that can run 24 hours a day in the hot, humid weather (oh, yes, we have that in Maine). It hibernates in the winter. Back in use now, infrequently when you switch it on, the motor hums, but the fan blades don't turn. If you leave it alone, and let it keep humming (not something I'm comfortable with doing), eventually it starts operating normally.
What do you think is going on here, and what should be done (other than taking the fan out of service and recycling what parts I can)?