Find logins in log

grep "A=login" /var/log/exim/mainlog

hostname --fqdn did not return a fully qualified name

fix /etc/hosts etc, but if hostname -f/--fqdn fails, run hostname mail.example.com and save yourself a lot of headache

Helo command rejected: need fully-qualified hostname

Make sure your FQDN/IP are ok in /etc/hosts

Message is frozen

Mail can't be delivered locally, check storage.

all relevant MX records point to non-existent hosts

This may mean the MX IP is a private one, in that case remove that IP/network from ignore_target_hosts

Show queue

exim -bp

Show body of message in queue

exim -Mvb 1gKM2x-0004ti-Lj

remove frozen from queue

exim -bp|grep frozen|awk '{print $3}' |xargs exim -Mrm