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I'm sorry to hear that.
I suggest that you raise this with your local support since warranty may differ from market to market. They can also give you information about how to proceed with this in the best possible way:
http://www.sonymobile.com/global-en/support/contact-us/contact-info/
Same happened with me too in sony xperia J..1st my screen broken that changed with local service center suddendly phone stopped working completely not even accepting charging. When shown to sony service centre they said its problem of mother board. Is sony only giving small life motherboards with its all handset.