How old is your phone? If it's sorta new, I'd say bring it back to the store. If it's older, bring it to whatever company's store (Verizon, AT&T, etc.) and ask them about it. If the on button isn't working, there isn't much you can do. kk4df might be right though. Try taking the battery out and reinserting it. Or, if you have a spare battery, try using that one instead.
Have you tried turning it on with it plugged into the wall? If it doesn't show you the battery % when it's plugged in, that is a bad sign.
