Wires often break from tugging inside the cable at the plug end - a common fault.
Begin by cutting away the plug and a few inches of cable - fit a new plug - just a few minutes and minimum cost.
If it's not a fix - and I would bet that it solves your problem - then you've lost very little.
You do not mention the model - but no matter - Dyson Medic might help you.
Good Luck...
December 2015