With a big capacitor illustrated, my guess is that the motor is an induction motor, not a conventional carbon brush type. With a failed condenser the motor will not work, as it needs this "start capacitor" to give the field windings generated magnetic field a little kick to align them with the AC current. Simple explanation for something quite clever.
The switch may also be faulty, well said Rob, so by-pass this for the time being. Plenty on the net about wiring an induction motor and test procedure. On the motor, two wires are the capacitor connection, yellow and black. The remaining black and blue pair are live and neutral. Trace back to the switch to see which is which.
When our central heating failed (Oil Fired, with induction motor on the burner), I substituted the start capacitor off a Belle Cement mixer, and that got the heating working. There's probably one in the washing machine.......and maybe one on your pressure washer or compressor.
Cheap as chips these days, all made in China.
May be something as simple as a loose connection or failed fools' repair. Duff fuse or mains lead also to be expected.
Swarfy.
PS Reckon a new shed is on the cards....