I have the same problem with my iPhone 6 and more to that. For sure Ive tried hardware restart (almighty 10 secs of two-button press), syncing with iTunes and updating firmware but the most annoying is to be limited with cellular data. But as I said, there is more: After I realized that WiFi switch grayed out, I also realized that following functions started not to work either.
-Bluetooth: does not turn on. dots keep spinning.
-Location Services: iPhone cannot locate itself.
-Date and time progression: This is the most interesting! iPhone clock for indicating the time does not change. it stays at the last time when it is manually set. Which causes that all the pictures taken and all incoming text messages are tagged with the same time are again sorted wrong.
-Display Rotation: Display does not rotate when iPhone is held portrait or landscape.
-Vibrate on silent: iPhone only vibrates when it is not muted.
I've listed all the items as I figured up to now. If I observe any thing more I'll post for sure.
Since it happened after warranty period, authorized Apple repair shops proposed swapping with a brand new iPhone 6 for $370
I did not see anyone has ever faced all those problems at the same time. I desperately search for some reasonable explanation.