Outlook ignores the specified account when sending mail

The PC is connected to a LAN which sometimes has access to a DSL internet
link. It also has a modem. Outlook 2003 is a POP3 standalone configuration.

I have a number of mail accounts configured. POP3 (read) access is
available, and works, on either the LAN (via DSL) or dial-up access. One
account has SMTP access over the LAN (via DSL) and the others can only access
their SMTP relay host via their respective dial-up hosts.

The problem I have is:
Assume the LAN currently has access to the Internet.
If I compose an email, select the LAN SMTP account from the accounts
dropdown and then send. The message goes out successfully, as expected.

If I compose an email, select a Dial SMTP account from the accounts dropdown
and then send. The message goes out via the LAN SMTP relay host and has the
LAN SMTP sender details. ie Outlook has ignored the selected account and used
a different one.

The LAN SMTP account is NOT the default account.

It does this irrespective of which dial-up mail account I select and even
when the dial-up accounts are configured to use the modem in the account
setup.

If I first establish a dial-up link then everything works as expected, mail
sent via the LAN SMTP fail as the host correctly rejects the login. Mail sent
via the dial SMTP works for the ISP I'm connected to and fails for the others
again as expected.

This machine previously had Outlook 2002 installed (not office) and was
upgraded to 2003. Outlook 2002 worked as expected either on the LAN or via
dial-up. I have uninstalled Outlook (and office) and reinstalled from scratch
with no change.

Can anyone offer any suggestions it is driving me potty trying to understand
what is going on.