by Ken Task.
The first time, did you get past the initial pages where the config.php file was created? Check to see if there is a config.php file in Moodle code directory. If there is it might have recorded the IP address as you accessed it the first time in the config.php file.
Best to install a Moodle to be accessed from the net with a FQDN - fully qualified domain name - which requires an entry in DNS.
One can cheat on that a little by editing the hosts file and creating an IP -> FQDN entry (the FQDN entry is the host name as it will be in DNS). That's IF the apache server config hasn't been set to respond to a certain IP address or hostname. On RH/CentOS servers, that is the default.- ie, not tied to an IP nor hostname.
'spirit of sharing', Ken