So you've had five folks on this including Apple? Um, OK. Chances of success here in the forums will be low, and — without some indication of what's been tried — we're going to be duplicating tests.
Definitely follow the troubleshooting information that Linc Davis's pointed to.
On no evidence, I'd wonder if there's an issue with the AT&T mail servers, or with reaching the AT&T servers from your local network. In particular, stay off of TCP port 25 for sending mail. That's usually tested with telnet or openssl s_client, depending on what's going on, though Connection Doctor should pick that up.
There's also been an apparent account corruption seen very occasionally, so if nobody's already tried this, entirely remove the account entry, and re-add it. This entails removing both the POP/IMAP connection configuration for receiving mail from the server into Mail.app, and also removing the SMTP/ESMTP connection configuration for sending mail from Mail.app to the server. Then re-add the connection.