1. First things first, To make things easier remove the bin from the front. Use a small flat tip screw driver to gently lever up the on/off button on the side closest to the handle. Be carfull as you may break the little wedge that stops it from coming out when you use it.
2. Under the button you will find a torx screw, If you don't have a torx driver that fits you may be able to use a flat head driver, Undo this screw and the button/cord unit can be then slid up and out.
3. If you can, Take a picture of where the wires go just incase you forget when it's time to put it back together. Unplug all connectors and remove your cable.
4. Cut your cable so you have about an inch of blue and brown cable left on each connector, Next cut away the broken section of cable, Strip away the outer insulation, to leave around 3/4 inch of brown & blue.
5. Strip the insulation of all four ends on brown & blue use one small terminal block, Maybe 3A or 5A for each colour.
6. Put all the wires back as they were, If this does not fit back in the handle remove the insulation from the terminal blocks, Be sure to use insulating tape if you do this.
7. Slide the unit back into the handle, if you have a flat or phillips screw the right size you way want to use this rather than the torx, If you have to do this repair again sometime in the future this will make it easier.
8. If you are unsure of any of these steps I will soon post a video on youtube, search for
"dyson DC04 cable repair".
or go to my page http://www.youtube.com/djdavies83
*All reapirs done at your own risk, The info in this answer is provided only as a guide and the author will not be held liable for any loss, damage or injury however casued*
youtube.com/djdavies83, August 2008