My guess would be that one of the inner cores of the cable has broken where the cable enters the machine. Depending which model you have they can be a nightmare to get into. Dyson have an excellent fixed price call out charge that covers parts & labour. They also usually have at least a 2 year warranty, but you do not say how old your machine is.
Check the motor filters, typical symptom of blocked filters causing restricted airflow to the motor which then overheats and shuts off (thermal overload) for a while till it cools down again.
Depending on the model you could have up to 4 filters in different places all will need checking and some should be replaced fairly often (depending on the use).
If you need to find a tradesperson to get your job done, please try our local search below,
or if you are doing it yourself you can find suppliers local to you.
Select the supplier or trade you require, enter your location to begin your search.
Please select a service and enter a location to continue...
Are you a trade or supplier? You can create your listing free at DIYnot Local