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Charge your phone for one hour then repair your phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
Also remove the SIM and SD cards > restart your phone and try again (w/o the cards)
You can also boot on safe mode, if nothing work then do try PCC
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
If neither PCC, safe mode or removing the cards work then contact your local Xperia Care or EE