As 'Champer' said first on the list would be to check the fuse in the plug, this can be done two ways by either trying a fresh fuse (new or from another working appliance) check it is the right amp fuse also.
when you have eliminated the fuse as the source the next logical step would be the the on/off switch.
Although you may think you have turned it on you may have a faulty switch that needs replacing.
http://static.yourspares.co.uk/media/p/qualtex/q/l/QUASW74.jpg
Best way to test it would be with a http://t2.gstatic.com/images?q=tbn:ANd9GcTjX7VUSo7zoY2zODFc9R5IQO20KajNTatGZUJQo9ADIOXwwhH4
Select http://www.evilution.co.uk/smartelectrics/brakeswitch/test/multimeter1.jpg and apply the prongs to each side of the switches terminals, turn off and on, if you hear a continuous beep when the switch is switched on then relax - it's not the switch.
Then next step would be to check the bushes on the motor http://www.appliancespareswarehouse.co.uk/image/cache/data/cat/vacuum/DYS905358-05_b-800x800.jpg
These are the black bits either side undone with a small cross-head screwdriver, if the bushes are worn out then the cleaner will NOT turn on, this can be remedied by simply replacing with new ones.
If the bushes are ok and not worn out, I've never really got that far so i'm not sure.
Here's an exploded diagram to help when disassembling johnny 5 and always remember to strip the machine down in a logical order this helps with reassembly with no bits left over.
http://www.vacpartswarehouse.com/Dyson-DC11-Telescope-Cylinder-s/3898.htm
Hope it helps. . . . . and remember Safety First - ALWAYS have the machine unplugged when taking apart.