Check the following...
Overheat reset button (if the machine has one)
Wall socket
Plug fuse
Plug wiring unless it's a moulded plug
Integrity of power cord
Then you need to dismantle the machine and check the on/off switch the termination of the power cord the motor brushes and the internal wiring to and from the switch. If all these things are OK the problem may well be a burnt out motor.
Repeated tugging on the power cord over time is a very common cause of a vacuum cleaner not working - the wires eventually fail. Consider how the machine is typically used - does the operator sometimes strain the power cord?
Your other options are to have it repaired or to buy a new one. Repair shops are quite rare so a local handyman - a retired gent with a technical background might be tempted to look at it for the price of a couple of beers.
Good luck...
Retired Gent, June 2009
