[exim] SMTP connect fails after network changes

There was some fiddling with the network around our exim 4.63 (old)
mailserver, and now I am unable to connect to send mail from
outside. I can connect from inside. The connection uses TLS to port
25 and authentication.

Evolution says "Failed to connect to SMTP server biostat.ucsf.edu in
secure mode: STARTTLS not supported". Thunderbird, from a different
location, has a similar problem. In contrast, this message was
sent via the same server from an inside client (a different exim
running on my machine inside the firewall).

Connection to the imap server on the same machine has continued
uninterrupted for all locations.

I can telnet (using telnet-ssh) to port 25 and get a response from
exim. So the problem is not that port 25 has simply been blocked.

Can anyone suggest what might be going on, or what we might do to
diagnose this further?

Thanks.
Ross Boylan

P.S. The network fiddling was done by a different group; I don't know
any of the details. They are likely to be more responsive if we can
point to a particular thing they can tweak.