DIAGNOSIS The main logic board has likely locked up—a minor software glitch. It's not uncommon after a brief power flicker or a long period of continuous use.
FIX Perform a hard reset. Unplug the purifier from the wall outlet. Wait at least 30 seconds (I usually wait a full minute). While it's unplugged, press and hold the power button on the machine itself for 10 seconds to drain any residual charge. Then, plug it back into the wall and turn it on normally using the button or remote.
IF THAT DIDN'T WORK If the screen remains dead but the fan still operates, the LCD display ribbon cable might have come loose internally. This isn't a user-serviceable fix. You'll need to contact Dyson support.
HEADS UP If you have it plugged into a smart plug or power strip, try plugging it directly into a wall outlet for the reset to rule out power delivery issues from your accessories.