When I uninstalled Outlook I edited the registery to remove all traces of
Outlook by doing a search and deleting all keys for Outlook before
reinstalling it.

I use Gmail and only have one account in Outlook.  Gmail receives mail from
old AOL accounts to my Gmail account and they are then forwarded to Outlook
into one inbox.

Under the registery key
[HKEY_CURRENT_USER\Software\Microsoft\Office\Outlook\OMI Account
Manager\Accounts]
there are three accounts listed:  1, 2, 3.  There were five, 2 of which were
under my name.  Those were the two I deleted.  

I am using Windows XP, SP3.  I have downloaded and installed all the updates
for Windows and Outlook, and had done this when I had the problem.  Nothing
fixed it until I edited the registry.

I'm not a computer expert but after being annoyed by the Enter Network
Password pop-up for a couple weeks, I was ready to try anything and this
seemed to work.  

Pat