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That's quite interesting, what happens if you now try the software repair process?
If it fails, then I can only really advise that the handset be sent to a service agent for repairs. That can be done by taking it back to the place of purchase or contacting Sony Mobile Customer Care from within your region.
I have a link in my signature below that will supply the contact details.
Have you tired performing a system repair using PC Companion
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
You had the same issue back in February
http://talk.sonymobile.com/t5/Xperia-SP/sp-not-working-wont-turn-on/m-p/944919#M35047
Please don't create duplicate posts as its consider SPAM
I took the liberty on merging the posts as it's the same issue that it seems it was never solved.