[exim] smtp authorization test via telnet?

Here are the symptoms:

The server is running cPanel. All domains except the first domain can send and
receive mail. The first domain can receive mail, but not send mail.

I can log into the user's POP3 account using telnet to port 25, then try to send
mail through the SMTP port, but as soon as I enter the "rcpt to:" address I get
the:

550-hostname.domain.name (localhost) [xx.xx.xx.xx] is currently not permitted
550-to relay through this server. Perhaps you have not logged into the pop/imap
550-server in the last 30 minutes or do not have SMTP Authentication turned on
550 in your email client.

(Obviously, the domain and IP address are not included here.)

This may be related to another discussion happening on this list, but I can't
explain why all the other domains can send mail and this domain can't.

Locally, exim -d -v user@??? and exim -bt user@??? both deliver
correctly.

So, I'm wondering if anyone knows how to check smtp authorization from telnet?

Virtual domains and virtual users normally do not have shell access. Is there a
way to execute exim in a verbose mode as if it were sending from a virt user?

Is there a way to get more verbose output, or more explicit output in the
mainlog?

Thank you for your help,

Mike Burke