Viola
Welcome.
This is curious. The half-moon symbol indicates that "Do Not Disturb" is activated (there isn't a snooze mode). But what puzzles me is that on my iPad Air & my wife's iPad 4, we have this function enabled, but can access our mail without any trouble by tapping on the Mail icon.
Of course, if you're back to normal, that's fantastic. But the "Do Not Disturb" function is really to silence any incoming calls (and I think, messages) and should not affect your ability to access mail, or indeed the internet via Safari.
Is there any chance that you were in "Airplane" Mode? Although the icon for that is, unsurprisingly, a picture of an Airplane! You cannot access the internet at all in this mode.
Strange; but solved, so great!
Ian