... it decided that I was not online, would not let me go online ...
It sounds as if something (a third-party browser, for example) has set the GlobalUserOffline registry value to True. With Windows Live Mail closed, launch Internet Explorer and press Alt-F to open the File menu. If Work offline is selected, click it to deselect it. If it's not selected, select it, wait a moment then deselect it.
Now try to launch Windows Live Mail again. Do you get the same error?
EDIT 1 May 2016
In 2013, this was a common error caused by interference from third-party browsers. This interference has been dealt with on recent versions of Windows (7, 8.1 and 10) so the cause of the error is now likely to be a different one. This answer no longer applies, except perhaps on XP and Vista.
Please see this wiki article for a likely explanation of the error currently being experienced by many users:**Error when attempting to connect to the Windows Live Calendar service**