This is what is known as the 'Yoke Loom Assembly' for the DC25.
Sometimes, when there is no power to the cleaner head, it will be one or both of the wires in this little loom that have broken internally. You can try to repair them, but they tend to fail again shortly afterwards because the repaired ones won't flex correctly. Better to replace this little loom and do the job properly.
Dyson used to supply this with the carrier (part number 916190-01) but discontinued it some time ago. This is supplied without the carrier as there is no need to change that, you only need to change the loom itself.
A link to our free fitting instruction video comes with this loom.