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If you are on IOS its probable the battery is flat - try charging it for an hour.
It should come on by itself, or tap the screen while charging to see if it responds.
There are know problems with chargers - check all 4 pins are equally prominent.
Have a look at the suggestion posted here it may help check if its a charging problem or watch.
If that fails and the watch is faulty try Fitbit Support. They may be able to help you with a replacement under warranty.
Author | ch, passion for improvement.