Given that this machine can't see the 'Net, where is it getting the name of the relay machine from ?
It can't even see DNS?
No, it can see DNS - on the mail server, which is running dnsmasq. But surely that will simply look things up - it wouldn't supply the name of a relay machine, other than the mail-hub it's been told to use.
Or is this an MX problem ? Is the old server asking the DNS for an MX record and being directed to the ISP's mail-backup server rather than coming straight through to the new mail server ?
It's as if it can't resolve the primary MX and is therefore going for the next one, relay-1/2.mail.demon.net. The strange thing is though that it should be using the smart host on your internal network rather than going for the MX hosts anyway.
Are you sure sendmail is using the right sendmail.cf file? ISTR that in old versions of Red Hat Linux, sendmail.cf was in /etc rather than /etc/mail
Paul.