DIAGNOSIS Complete power loss points to a failed power supply unit (PSU) inside the base or a tripped internal thermal fuse.
FIX First, try a different wall outlet. If no change, check the power cable. It detaches at both ends. Ensure it is fully seated in the socket on the purifier's base. Try a different cable if you have one.
IF THAT DIDN'T WORK The internal PSU has likely failed. This is not user-serviceable. You must contact Dyson support for a base unit replacement.
HEADS UP Do not open the base. The PSU contains capacitors that can hold a dangerous charge even when unplugged. There are no user-resettable fuses inside.