Mailboxes (presuming you mean an Inbox) go offline for a few reasons: 1. The server is down, 2. Your network is not connected, 3. Your password is wrong, or changed, 4. Just a glitch in the connection. Typically #4 will fix itself, eventually. #1 you have to wait for the server to come back online. But 2 and 3 you can check for yourself. To check the network end to end, you can open Terminal and use "ping <<server name>>" where you change <<server name>> to your mail server to see if the route to the server is found. If it is, the network is working and you have connectivity. If it doesn't check that you haven't misspelled it and if you are confident, you can call the mail provider to ask what is going on. (Actually, you can do that anyway and they can eliminate #1, Check #3 and maybe help with #4. #2 is going to be tougher, but the fact you got here sort of implies that your system is connected to your LAN and that is then connected to the Internet, so that should be ok.