I've got an old bandsaw which has a bit of an issue. It's nothing fancy, just plugged into a standard 13amp socket. The basics : The 'on' button on the switch box can only be depressed when there's power to the machine, thats fine. When you power it up it 'hums' when it's not running. You turn it on, you turn it off - all good. But occasionally the 'hum' won't be there when it's plugged in and the on switch can't be depressed. If you wait a minute or two it'll work again... at least that's how it normally is but the last time I used it I waited a good 10mins or so and couldn't get it to work again so moved onto other things. When it won't run there's no hum from the machine and the on switch has no 'click' to it. But tested it again today and it worked perfectly. There's the hum when it's powered up but not running and the on switch can be used. Sound like a motor capacitor issue? I've replaced such things on an old tumble dryer before. A new capacitor is dirt cheap, so it's an easy test anyway - just thought I'd ask around and see if anyone knew about such things. https://www.bedfordsaw.co.uk/spare-parts-for-elektra-beckum-bandsaws
From your description probably not the capacitor. I am guessing that the hum is from the magnetic seal in circuit for the on switch. The absence of the hum suggest there something wrong with the switch mechanism. Hope that helps.