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I'm sorry to hear that. I suggest that you try to repair the phone software using PC Companion..
Before repairing your device you may want to backup your information first. Check out this topic for more information on how to.
How to backup?
If the issue should still remain I think that this needs to be examined and fixed at a repair center. For more information about how to submit your phone for repair and where, contact your local support team.
Best regards,
If you're using Mac we have a software called Bridge for Mac: http://support.sonymobile.com/global-en/xperiaz3/tools/bridge-for-mac/
Best regards,
Unfortunately no, it's not possible to downgrade to a previous software version.
Unofficially you can downgrade but you need a firmware file and a program called Flashtool - If you Google manual update using Flashtool or Debrand using Flashtool then you'll find lots of guides and firmware can be found on XDA or Google Xperifirm which you'll find on XDA or see here ignore the title but do follow the guide
You should also take a look here:
/t5/Xperia-Z3-Z3-Dual/No-service-after-Lollipop-update-Xperia-Z3-D6653/m-p/980062#M15635