I have clean the filters thoroughly but it keeps cutting, and now has stopped working completely.

how do I get it to work,please?

Sam P., April 2017

https://www.dyson.co.uk/support/dc34/dc34-animal-exclusive/my-machine-is-not-working/machine-won-t-switch-on-or-cuts-out/thermal-cut-out

http://www.dyson.co.uk/support/dc34/dc34/my-machine-is-not-working/maintaining-your-dyson-machine/maintaining-your-dyson-machine

acp, April 2017

A very common problem with vacuum cleaners is a broken conductor inside the cable - at the plug end - caused by over enthusiastic tugging over time. I have fixed perhaps 10 cleaners by simply cutting away the plug and a few inches of cable and by fitting a new plug. Quick cheap and simple. Even if it doesn't cure your problem the effort is minimal.

Another issue may be the over-heat cut out operating when it should not - these things test the temperature of the motor and will be fixed to it - you may have a temperamental one.

Other than that - as you say - the internal filter which you've cleaned.

Good Luck..., April 2017