I'm not happy that I had to, but I've solved my own problem.  The
problem was: how to make an HTTP type e-mail account behave in Outlook
as though it was a POP3 type, because Outlook treats HTTP type
accounts as second-class citizens (and Brian, you're wrong to
disagree).  As late as Outlook 2007, the program will NOT allow an
account set up as HTTP (web-based e-mail) to be the primary mailbox,
even if there is NO other account set up.  It will force the creation
of a SECOND Inbox for the HTTP account, leaving the "primary" mailbox
empty.  SECOND CLASS treatment.
Any PDA's out there have a hard (impossible, to my knowledge) time
synchronizing to anything other than the primary mailbox.

But there IS a fix!

This inexplicably difficult behavior was first caused for me by my
making the mistake of installing MSN Explorer on my computer when I
upgraded to DSL years ago.  In  the fine print (I'm told) was a notice
that by doing so, my perfectly functional POP3 e-mail accounts would
be IRREVOCABLY converted to HTTP.  Not in the fine print was the fact
that Outlook doesn't like HTTP and my use of Outlook would be broken -
period.  All because I installed MSN Explorer (the butterfly).
Afterwards, when Outlook stopped downloading mail, I suffered though a
number of hopelessly undertrained "tech support" personnel, to no
avail.  I gave up and used MSN for years, which was Microsoft's
attempt to compete with AOL, and has the same childish interface.  The
teenage girls are thrilled.  But I suffered with a huge loss of
functionality, and an intrusive program that never stopped trying to
SELL me something, and added more Microsoft based glitches to my
computer, like the mysterious Connection Center, which has somehow
installed itself twice over the years, and then pops up incessantly,
trying to connect via dialup!  Not to mention the glitches caused by
MSN Messenger, also directly related to MSN Explorer.

Brian suggested "solving" the problem by installing yet more related
software, the Outlook Connector, and possibly having to sign up for
Microsoft Outlook Live.  With that as the only "solution", I was
shopping for a new e-mail service provider when I stumbled onto the
solution, which, almost ironically, Microsoft has provided.  But why
didn't you mention it, Brian?  Is it a well kept secret?

Microsoft has a (new?) server to allow HTTP e-mail accounts to be
treated like POP3.  It's called pop3.live.com.  Here's how to fix the
problem:

Go to Microsoft Support, look up Knowledge Base article KB930008,
follow the instructions in Method 2 EXACTLY (use the same settings for
either Outlook 2003 or 2007).  I've provided a link here:
http://support.microsoft.com/kb/930008

Here are a few details you want to be sure not to miss:
On the initial email creation screen, be sure to use your ENTIRE e-
mail address as your User Name under Logon Information (it auto-
populates with just part of your address).  Do NOT check to use SPA.
In 'More Settings' on the Outgoing Server tab, check the "My outgoing
server requires authentication" box, and "Use same settings as my
incoming mail server" (important or you can't send mail!).
On the Advanced tab, check both SSL boxes and set incoming to 995,
outgoing to 25.

If you plan to ever access your e-mail from more than one machine or
program, you need to know this:
A fundamental difference between POP3 and HTTP is that POP3 normally
downloads ALL messages to the local computer, leaving nothing on the
server, so if you later try to look at your (undeleted) e-mail from
any other machine (or program), those messages are gone - they're on
the machine you downloaded them to earlier.  HTTP was created to allow
multiple access points (web-based), so all e-mails are stored on the
SERVER until deleted.
But by using the following instructions  (which aren't in the KB
article), you can make Outlook play well with HTTP based access: you
can still access the account from the web (like Hotmail.com).

On the Advanced tab, check "Leave a copy of messages on the server"
and "Remove from server when deleted from 'Deleted Items'".  These two
options will make it work like HTTP.

I have Windows XP SP1, and Outlook 2003.  I'm confident this method
will be virtually the same for XP SP2, and Outlook 2007 or any
arrangement of those.