The rear hose on a DC04 usually splits inside the cuff at the wand end. Remove the wand and stretch the hose enough to see the coils inside the wand cuff. This splitting is caused by the metal end of the wand rubbing the hose when you clean stairs, skirting etc.
Gordon
September 2006
Have you checked whether something is blocking the hose? Not sure what your Dyson looks like, but if it's like mine it will have one or two little plastic flaps at the base of the hose. If something like a small pebble or a button gets stuck in there you may lose power - try having a look there.
Otherwise there may be a build up of fluff in some other part of the vacuum.
Good luck - Jill