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Repair your phone with SUS or PCC
Update Service (SUS)
PC Companion (PCC)
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
If that doesn't work then take it to a Sony repair center
Also, open all the cover/flaps and look for a white rectangle in each compartment, if its pink or red then there's water damage