This is a post just to help anyone who might experience the same:
Yesterday, after a new firmware update, my Xperia Z3 would not give me any mobile data. Calls, and Texts were fine!
Disabling and re-enabling Mobile data & Roaming had no effect.
Soft Reset of the phone had no effect
I got the phone while living in Germany, and am using it on the 3 network in the UK, this didn't seem significant until after I replaced the UK SIM with the German one, restarted the phone and it reconfigured for the new network, and Mobile Data sprung into life.
Replacing the UK SIM back into the phone, the configuration updated again, and everything started working, including LTE.
I would suggest that the firmware update overwrote some important configuration, or altered the NVRAM settings. I'm not sure how to force the reconfiguration without a second SIM, but it would be good to know.
Good luck if you experience this, and I hope it helps.
