I have a similar "Internet unreachable" problem with 3 different versions of iOS: 8, 9 & 10. Unfortunately I can't reproduce it. The same problem occurs with 2 different mobile phone operators.
Here are the common facts I was able to register on an iPhone 6 running iOS 9.3.1.
- Mobile phone network is OK:
- All other possible Network connecions are off (Bluetooth, Wi-Fi).
- Any web browser give an error message clearly stating the Internet is unreachable:
- All other application using the Internet are endlessly looping without any clear error message.
It is clear that the iPhone either doesn't have a valid IP address or doesn't have a correct routing information to reach the Internet.
In such a case how to diagnose clearly if the problem is a software failure coming from iOS or a failure coming from the mobile phone network?