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Contact your local Xperia Care as it could be a hardware issue
Few other things you could do is to repair your phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
boot on safe mode
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
Does your phone has a protective case or film?
Remove them and check again
You should contact your local Xperia Care