One obvious difference I see is that the HTML version loads http://tikvatisrael.org/js/tiny_mce/themes/advanced/link.htm in the popup, while the perl version loads http://www.tikvatisrael.org/js/tiny_mce/themes/advanced/link.htm. (note the leading www)
Update: And to confirm that this is indeed the problem, load the perl version by going to http://www.tikvatisrael.org/cgi-bin/tinymcefull.pl instead of the www-less version and you'll see that everything works now.
I'm guessing it's some cross-domain protection code kicking in.