Hi,
Did you checked the cPanel config file (/var/cpanel/cpanel.config) and change port 80 in apache_port assignment to 81:
apache_port=0.0.0.0:81
In the mean time run the command "/usr/local/cpanel/whostmgr/bin/whostmgr2 --updatetweaksettings" and check is the domains are working or not.
If its not check the apache conf file /usr/local/apache/conf/httpd.conf for any occurences of port 80, and run /scripts/rebuildhttpdconf to make sure httpd.conf is up to date.