Hi, I am A. Stevens here to help with your question!
So all we would need to do is to set up the account again in Mac Mail using the Time Warner server info and your username/password. Depending how you have Eudora setup, it may or may not sync the contacts over, but to make sure what you can do is export that data and import it to Mac Mail.
We could arrange for additional services for a remote screen sharing session so that I can assist you to do this while you watch
OK...I am trying to assist but there are steps involved...if you want to cancel no worries.