E-mail Accounts Working Again !!!
Finalll Resolved the Issue ... !!! As I suspected, it was something incredibly Simple .... !!!
To the right of each E-mail Account in Mail, there was a "Tilde" sign to the right, indicating that there is something wrong with that E-mail Address.
Finally, DreamHost Escalated my Issue to a higher-up Tech Support. After trying many things, most of which I had already been trying with other Techs all day long, finally the Tech told me to right click on the Tilde, and choose
"Take Account Online"
which worked for five of the accounts, but still had issues with the last account, which finally got working.
So what could have been the cause for this Problem to Happen?
I know that somebody did hack into my E-mail Account, because the first Tech this morning gave me some of the characters to my Password (very long Password), but those characters did NOT match up with my Password!!!
Has anyone run into an E-mail Hack like this one ... ???