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Hi,
Have you tried to connect manually to these networks or have you tried with three different SIM-cards from these providers? If you only have tried to connect manually, I suggest that you try another SIM-card in your phone to see if same thing happens.
Try this
repair your phone with PCC > do NOT install any app > uninstall any antivirus > don't even enter your google account > try to see if that works
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
I remember other users complaining about a similar issues, it seems that the SIM card might be to thin, but it'll be wise to get a brand new SIM card.