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Is there anything blocking the proximity sensor?
Can you try settings-apps-all,scroll down to incall ui and tick show notifications?
Boot in safe mode:
/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
Does the same occur?
You could repair your phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355