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Check that the battery is charged. Charge it up for longer than 2 hours continuously, then try again. Also, if the charger is the type that plugs into the phone, rather than the type that requires the battery be removed from the phone for charging, see if the phone will turn On and work OK when the charger is attached to it - if it will, don't run it for long that way, but if it works that way for a few minutes, then the battery is bad, quite simply, and would need replacing for the phone to work normally again.
If it does not turn On even when plugged in to the charger, then let me know how old it is, measured from its date of purchase.
Your account is not clear to me.
Does it turn On, with the battery still in it, when connected to the charger?
If it was purchased in June of last year, its warranty has expired, unfortunately.
If you have Google Contacts, then your contacts are, most likely, stored on Google's servers, not just on your phone, and thus would not need recovering from it.
Does your phone have a memory card inserted in it?
Was the phone gotten wet, or damp? was it used in very hot (95 degrees F. or higher) or very cold (below freezing point) circumstances? was it dropped or otherwise subjected to mechanical shock against a hard surface?