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Settings > Xperia > internet Settings
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Hope its a settings issue, check if you have correct settings if not download settings with your Network Provider, Install settings and restart your phone...
I also have this problem with my Xperia Z tablet 321. My network operator (Ovivo) appears in settings>mobile Network Settings>network operators but in Xperia>internet settings>Select operator, it does not
I chose the network that carries Ovivo (Vodaphone, I believe) and the Xperia downloaded the internet and MMS settings. I restarted the tablet but Firefox and Chrome both continue to say I am not connected or am Offline.
I'm not convinced this is a settings problem as the tablet shows 3-4 bars mobile signal - it may be due to the network operator?
Vodafones internet settings will probably not work if your subscription is not from them. Try setting up Ovivos settings manually according to this instruction: http://ovivomobile.com/wp-content/uploads/2013/05/OVIVO-Mobile-Android-Phones-Setup-Guide.pdf
I am having this problem since friday. I've had this problem before but it was a bit different then. Last time when I had this problem it was I didnt have any reception at all after many factory reset it finally found the reception and then it worked. But this time it finds the reception but I dont have any internet (no Edge, H or H+ or 3G) I have full reception. I've downloaded the apn settings still not working and its not sim fault as I tried that sim in my Galaxy S2, it works like a charm no problem at all. What could be the problem. Why did it stop all of a sudden? I'll reinstall 4.2.2 again lets see if it works. Fix it sony.