If you've checked your settings, chances are that your dial-up provider prohibits it.
Several ISPs prohibit what is known as mail relay. Mindspring is one or them.
They require that when you send mail through there dial-up that you use the SMTP setting they provide. To see if this is the case, change the SMTP according to their set-up instructions. If the mail goes through, then that was the problem.
You can leave your email program to that SMTP setting, and indicate the return email address of your domain. With the exception of checking the email routing headers, most recipients won't know the difference.
The only other solution is to change to another dial-up ISP.