When I try to get my messages off of my POP mail server,
it does not bring down old messages that I read through
the server's online interface. Is there a way to get all
of my old messages?
Yes. Go to Tools -> Accounts, open your POP account, click the "Options"
tab, and press the "Get all messages left on server" button.
Should I try IMAP instead?
If you're ISP offers it, that would be a good idea. With an IMAP, you
always see the full server contents.
If your ISP does not offer IMAP and you still want to view your server
contents, go to Tools -> Accounts, open your POP account, click the
"Options" tab, and check the option to "Allow online access". This creates
an icon for your POP mail server in the Folder List. Click it to access
your server contents. It is not as flexible as IMAP and not as pleasurable
to use regularly, but it is adequate if one needs to download a message from
the server on an occasion.