What happens when you switch to a different region to play?
This error indicates that the connection timed out, so it may have something to do with the way the school's network is setup.
You may need to check with your school's admin to ensure that all Diablo III ports are open properly.
I have the same problem, I'm on the Americas server. There was a patch earlier that asked me to restart the launcher, but it didnt patch anything. When I logged in, there were 80+ people on the server and yet no public games, 0 players for any quests. So, I decided to go solo, but there was an error that couldnt create a game. I logged out, tried to log in, but this time I had this error.
I couldnt connect to Battle.net. I am playing in my house over the past few weeks and this is the first time that this happened. I tried to change regions, I got through, but of course I have no character there. I tried on the Americas region again, then I couldnt connect to Battle.net.
Hope you have the solution for this, especially that it might be connected to the weird patch. Thanks!