A lot of older versions of Eudora don’t support authenticated SMTP. You should make sure you’re using the newest version available for your platform. Then make sure that you have any configurations for ‘Authenticated SMTP’ set.
You should also doublecheck that your ISP doesn’t filter port 25. If they do, you would definitely need to use their mail server. In fact we generally recommend that you use your ISP’s SMTP server if possible, although with DH2 we do now offer authenticated SMTP as an option as well.