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you should
you can also repair your phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
Performing a software repair using PC Companion.The process will erase all internal memory.You might need to charge your device for about 1-2 hours before so the device has at least 60% battery.
Make sure the device is not connected to computer or laptop and turned off (sometimes you have to press power button and volume up until the device vibrates 3 times or on some devices you have to press the small button near the SIM tray or on the back of the device).
Open PC companion->support zone->phone/tablet software update->repair my phone/tablet blue highlighted.Follow the steps given,do not connect your phone until prompted to press volume down while plugging USB cable. If PC companion does not start the repair process, you might need to run it in compatibility mode with Windows 7 (in some cases XP).
Backup if you want with one of the suggestions from uli.
I actually had this problem and I fixed it!!! on my phone the screen would shut off when i make a call and would not turn on no matter what. hope this also works for all of you.
Turn off phone
Press firmly on proximity sensor
Turn on phone
Once on main screen
Press firmly on proximity sensor
Try to make a call
I hope it works for you