If you are unable to log in to any of the webmail clients, start by checking the secure log.
If you see something like the following:
dovecot-wrap error changing uids: error: 1 (Operation not permitted)
This means that the dovecot-wrap program has the wrong permissions set. To resolve this, you will need to set the suid permission on that program. You can do this by issuing the following command:
chmod 4750 /usr/local/cpanel/bin/dovecot-wrap
This will set the correct permissions and resolve the issue.