I take it that they have also include_once() disabled, because that would be the most fitting alternative.
You could also try to open the files by file() or fopen() and eval() their contents, like
$fileContents = implode("", file("external.php"));
Of course external.php must consist exclusively of valid php code, that means no opening <?php and closing tags inside etc. Sadly, if your host has all include... functions disabled, I assume they have the filesystem functions disabled as well.
On some apache servers you can set those php configuration values directly in a .htaccess file. More info about that can be found at http://za2.php.net/manual/en/configuration.php
. This option can also be disabled by the server admin and depends highly on each single configuration of the server your script is running on.
For me it seems your host has a quite restrictive safe_mode configuration working (see also http://za2.php.net/manual/en/features.safe-mode.php
and what *could* be done to circumvent this). Frankly, I would write them a polite email and request that they reconsider their PHP security configuration. Because include and require are essential for PHP programming, unless you want to rewrite every script of yours.
If they still refuse to change their security policy, ditch them and change hosts.