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Are there not any reaction at all if you press and/or hold the ON/OFF button down? If not, it sounds more related to a hardware problem that a technician at an authorized service center needs to examine and fix.
Thereby, I suggest that you visit nearest service center to have the phone examined by a technician. You can contact your local support team for further information about nearest service center and/or how to proceed with this in the best possible way:
http://www.sonymobile.com/global-en/support/contact-us/contact-info/
