Be safety aware
Remove the power from the machine by disconnecting it from the wall plug, when you attempt the following
Use a DMM (Digital Multimeter - Ohmmeter function) to test the continuity of the wiring from the plug to the motor in the vacuum cleaner.
If you place the Ohmmeter between the 2 power pins on the plug (active and neutral) and turn on the switch in the vacuum cleaner you should get a reading on the meter.
If you don't you have a fault between the plug and the motor. You then need to do point to point testing with the meter to find out exactly where the problem is. Try connecting the meter to one pin on the plug and then prove continuity of the wire by using the other lead connected to the Ohmmeter and finding the other end of the wire either on the On/Off switch or on the motor terminals.
If you cannot find it by using the meter try connecting the meter to the other pin on the plug and see if you can identify it in the machine.
You need to prove continuity of both wires all the way to the motor terminals in the machine.
If you can with one but not the other it is open circuit and you will have to find where it is broken.