Note: Before doing anything listed here, you should take it to the place you bought it, or contact your carrier or manufacturer if it is possibly still under warranty. Many of the things listed here would make a warranty null and void, so check with them first.
There can be (on some devices) a small pin hole that will reset it.
However, have you tried holding down the power button for around 20-25 seconds? Also, are you sure it is fully charged? If it isn't fully charged it may not turn on.
If this doesn't do it, the problem may be the button, the charger cord, the charger port, or the battery.
Make sure the power button isn't stuck and it is actually moving the internal button ( the outer 'button' is just a cover to the internal...