It sounds like you may have set up the second computer to download your email to a pst, pulling it off the server. In that case it would no longer be viewable from the original computer. Is this an exchange account or some other email system account?
exchange 2003, mail client = outlook 2003
If you are using Exchange and outlook, you can import your pst’s and turn off the download ( probably archiving).
Make sure you don’t have a rule that deletes the message.