mac mail can receive but will not send outgoing mail

I can't send outgoing mail and my 3 mail accounts are indicated as offline. The options I have in the menu is to take them offline. When I do that (even though they are shown as off line) nothing changes except that I can tell them to go online, which they do not do.

The SMTP connection is the same as my wife's (different login) and if I click on the SMTP connection that "failed" it connect perfectly.

The genius bar has eventually corrected this twice before but it has not "stuck".

One last point when I bring this computer to the store the problem clears because it logs into the APPLE server. Help!!!!