Cut away the plug and a few inches of cable and fit a new plug.
May sound silly but this has fixed three quarters of the vacuum repairs I've done - the wires get stretched inside the cable from tugging - eventually one of them snaps in two.
Even if it doesn't work your loss is 10 minutes time and a plug.
After that look to the on/off switch
After that look to the over heat cut out being permanently open
After that look to the motor - but you would have noticed the burning smell - so forget the motor.
Good luck...
J Edgar Hoover, September 2014
