Digging around a bit I found this article: http://support.microsoft.com/kb/195730
What you can try is go to to
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Internet Settings
in regedit and backup the registry key (read the Help file for regedit to understand how to use it, if you haven't before). Then prior to running any programs you can try to merge that key and see if then, when you start IE or OE, they start in Offline mode.
The value name is for the "GlobalUserOffline" and the value of 0 means online and 1 means offline.
See if that works. If not, you may have to do it work HKEY_USERS as the article describes and then you'll have to figure out the proper SID, but then you can do the same as I suggest above for that key and it should work.
steve