Diagnosis
This is almost always a filter or power supply issue. The thermal cut-out can trip if the filter is blocked, or the power cord/connection at the handle is the weak point.
How to Fix It
First, unplug it. Flip it over and pop off the rear magnetic filter. Give it a solid tap over a trash can to dislodge lint, then rinse it under cold water until it runs clear. Let it dry COMPLETELY for 24 hours—no shortcuts. Reattach it, making sure it clicks into place. Plug it into a different, known-good wall outlet and try the power button.
If That Didn't Work
Check the power cord connection at the base of the handle. Wiggle it gently. If the light flickers or it briefly powers on, the internal wire connection is likely broken. This requires a service repair; Dyson will usually handle this under warranty if it's within the timeframe.
Heads Up
Never, ever use compressed air to clean the filter. It can force debris deeper into the mesh or damage the micro-filters behind it, which is a much more expensive fix.