If you are having problems starting apache on a non-standard port you might find that the problem is related to selinux.
Type this command to check to see what http ports are currently allowed; (remove filter to show all rules)
semanage port -l|grep http
To add another port type the following (with the port you wish to add etc);
semanage port -a -t http_port_t -p tcp 81
If you want to disable selinux completely then go into /etc/selinux/config and set selinux=disabled. Save then reboot.