The most common problem I've seen on the vacuum cleaners that I've repaired (75%) is a broken wire inside the cable and close to the plug.
This is caused by continual over enthusiastic tugging - the wires stretch and eventually break.
Your machine may have a different fault but the effort and cost to cut off 6" of cable and the plug - and fit a new plug will be minimal.
Vacuum cleaners have a over-heat safety cut out switch that self resets - sometimes (very rarely) they fail but this will not be the case in your situation.
Happy New Year..., December 2014
