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It sounds very strange that you experience this on other Wi-Fi networks as well, but its working via mobile networks.
I suggest that you try to reinstall the phone software using Update Service..
Before reinstalling 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.
You want to recover some of your files?