Everytime I try to send an Email, I am receiving the identical message. I will be replying to one posting, to one recipient and this is the message I get back. I believe the actual Email is going through, however. but need to figure this out.
The message could not be sent. The authentication setting might not be correct for your outgoing e-mail [SMTP] server. For help solving this problem, go to Help, search for "Troubleshoot Windows Mail", and read the "I'm having problems sending e-mail" section. If you need help determining the proper server settings, please contact your e-mail service provider.:

The rejected e-mail address was 'jobs@elitemanagmentconcepts.com'. Subject 'Entry Level Assistant Management In Training Opportunities!!', Account: 'pop-server.tampabay.rr.com', Server: 'smtp-server.tampabay.rr.com', Protocol: SMTP, Server Response: '450 4.1.8 - Domain of recipient does not resolve [R0309001]', Port: 25, Secure(SSL): No, Server Error: 450, Error Number: 0x800CCC79

Spelling the email address right always helps
check the spelling!
'elitemanagmentconcepts.com' vs 'elitemanagementconcepts.com'

That is the same exact message I receive, right down to THAT email. It has nothing to do with the Email being sent to. For example, if my recipient is abccorp.com, I will get the message, using jobs@elitemanagmentconcepts.com as the problem.

...because there is NO SUCH DOMAIN as elitemanagmentconcepts.com

If you send it instead to jobs@elitemanagementconcepts.com it will work - assuming the user exists.

My email address book has vanished! Can you help?

Nope - sorry.
Start a NEW thread of your own, and include details of your OS, and email client, and what you'd been doing leading up to the problem surfacing.