Share your experience!
This could be a network issue, perhaps a faulty SIM card, what if you manually enter the APN settings?
What if you reinstall the latest update with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
Hi Stina, welcome to the community!
Follow @Uliwoolys advice and keep us updated. If the repair doesn't work then you may need to try a different sim card in the handset, otherwise contact your local Sony Xperia Customer Care team.