Are you sure those links you posted earlier are correct... From my end both of those links give me "Sorry, page cannot be found..." errors...
you can also solve the problem from the other direction... figure out the actual directory of the forum files and from that determine what the forum directory needs to be based on the DOCUMENT_ROOT.
As far as waiting for your domain name... I don't think it will solve this issue but the domain name could affect the phpbb and Joomla configuration (especially for cookie settings)
Is that the setting for $mosConfig_absolute_path or "Absolute Path" if your looking at the Configuration page SERVER tab..?
Interesting how the paths look different from Joomla and from your error message...
/home/frozenhe/public_html from Joomla
/home/cyberho/public_html/~frozenhe/forum/extension.inc from the error message...
one is in frozenhe and the other is in cyberho... Is there something else different with the way the server is setup? It looks from the paths that they are installed under different users (accounts) of the server... Sure you don't have some redirects or something else happening?
Run that previous script from the Joomla directory and let me know what that returns for DOCUMENT_ROOT...