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The screen/phone doesn't unlock when you swipe to unlock it?
settings > about phone > diagnostics > test the screen.
Do you have any antivirus? taskillers? third party home launcher ? third party lock screen? any protective case ?
you can also boot on safe mode > try to recreate the issue
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
if you can't recreate the issue while on safe mode then it's a third party app that's causing this issue.
I think it's an app acting up, it'll be wise to boot on safe mode overnight and see if you experience the same issue, or, repair the phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355