A simple test can be done with a light bulb.
1. Remove to the fuse from the plug and try it in a lamp or something else that you know works. If the kit now doesn't work you know the fuse needs replacing.
2 Wire up a light mains light bulb, a downloghter socket is ideal, alternatively a lamp with a long flex.
Now take the brown wire from the light and screw it to the positive terminal where the mains enters into the motor. Remove the wire of the motor and wrap insulation tape around it. Wire the blue wire of the bulb into the plug of the extractor (blue wire in the plug, bottom left). Make sure there area now bare wires, keep pinkies well away and turn on. If the light illuminates you have power to the motor. If not, and bulb does not illuminate the wire from the plug to the motor is damaged and needs replacing. If the bulb does illuminate either the starting capacitor or the motor is shot. Ask your mate with the multimeter to check the capacitor / motor windings.
Note, there is normally a thermal cut out that can have tripped. Sometimes the is a button somewhere on or near the motor to reset it. The manual will give details.