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I'm afraid to say that in these circumstances the only way I know of to fix this is to perform a system repair which will also install the latest available firmware so best to backup before proceeding should you wish to
Performing a system repair using PC Companion - 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
Hi,
You could try to boot your phone into safe mode to see if the behavior may be related to any 3rd party app that you have installed in your phone:
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
If you can't minimum backup your external storage if any,
Update Using PC Companion
With a cable using a computer
Download and install new software using a computer application and connect the device to your computer using a USB cable.