Background
When you have network or email server difficulties, Apple OS X Mail can take itself offline.
In this state new mail is not collected and sent mail does not go out.
Visual Indicators
Mail may be online. The clock to the right of a folder tells you that messages are downloading and you should be patient.
However, if you see a squiggle to the right of Inbox, then Mail is offline.
Resolution
Tell OS X Mail to go online. There are slight variations in different OS versions, but the principle is the same.
In each case, go to the Mailbox menu and tell your program to Go Online.

The example above has an online/offline toggle. That is, the command changes with each click.
The command says 'Go Online' which means you are currently offline and cannot send or receive.
In other words, to be online with functional email, you want this to say the opposite, i.e. 'Go Offline.'
Yes, it's as clear as fog. That must be why the menu was changed. See the newer OS below.
There are two distinct choices in this second example.
The gray choice is the current state. Mail is offline in this illustration. You cannot send or receive.
The bold choice is available, and in this example it will take you online.
Maintained by Brien G. Muller
IT Help Desk,
Skidmore College, Saratoga Springs, NY
Revised 10/25/2007