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Hi @Rk5
I suggest you check this link:
http://talk.sonymobile.com/t5/FAQ/Backup-amp-Transfer/m-p/407253#U407253
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I'm at disposal for any question.
Best Regards,
I'm sorry to hear that, if the phone doesn't boot up, you won't be able to access your contacts, with that said, by any chance did you backed up your contacts with Google?
on a computer > access your Gmail > contacts