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Well, since the error is generated by the server and not Xoops, I'm inclined to believe that there is a file permission problem somewhere. You've eliminated XOOPS as the cause by installing a fresh default copy + you said the *server* is giving you the access error.
Really, the only thing that is left to do, IMHO, is go through the affected directories and files one at a time and check to be sure the permissions are set properly. The FAQ article
Here gives a very clear explaination of how you should set the file and folder permissions.
Sorry, but I don't know of any other cause for a server access denied error other than file permissions or an .htacess setting. It's highly unlikely that your host is denying access to /modules/system/admin.php, so it stands to reason that it's a file permission problem.
Maybe someone else has an idea?