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Remove your Sim and SD cards and check to see if the same occurs as this is normally associated with faulty cards
Your last option is to try performing a system repair using PC Companion as this will often fix issues - This will factory reset your phone and erase all data so best to backup before you begin
Switch off your phone and unplug from Pc (Hold volume up and power for around 10 seconds)
Start PC Companion and select Support zone then Update my phone/tablet then in Blue Repair my phone/tablet and follow the on screen instructions - When prompted connect your phone still switched off holding volume down or back button - This should start the repair or reformat process
If you are using Windows 8/8.1 or a 64bit operating system then adjust the settings for PC Companion and run in compatibility mode and chose Windows 7 or XP
If that fails then I'm sorry to hear this but you would need to either return your device to the place of purchase or contact Xperia care and have your device inspected http://www.sonymobile.com/global-en/support/contact-us/