Diagnosis
Hair, dust, and product gunk have solidified inside the button mechanism, jamming it.
How to Fix It
Unplug the styler immediately from the wall. Let it cool. Use a can of compressed air (like for keyboards) and blast short bursts at an angle into the small gaps around the stuck power button. This can dislodge debris. Follow up by working a toothpick gently around the button's edge to pry any sticky residue loose.
If That Didn't Work
If the button is mechanically broken—feels like it's collapsed inside—the switch assembly is faulty. Do not attempt to take the styler apart yourself, as this voids warranty and exposes high-voltage parts. You must stop using it and seek repair.
Heads Up
If the styler is on and you cannot turn it off because the button is stuck, you must unplug it. Do not just leave it plugged in and heating indefinitely, as this is a fire risk and will trigger the thermal fault.