Caps do not just hum...unless they are doing background for a barber shop quartet.
Seriously, pull the cap and take it to a shop and ask someone to put it on a Hunter, it will tell if the cap is any good.
If you know the size, PM me and I might just have a replacement. I have a few left and may have the size you need.
Last time I had this problem, and it was about the same as yours, it turned out to be the motor.
Hope this helps.
