So when you type http://localhost:81/cgi-bin/hellothere.pl into your web browser (for the simple perl file I pasted in earlier that simply printed a line of text, you get a download option instead of getting a simple webpage? This is expected because the content type is specified to be "Content-type: text/vnd.wap.wml"--which your browser on your computer can't understand (but your phone or a WAP emulator can understand; see page one of the article). Try replacing that line with "Content-type: text/html\n\n" and your browser should then be able to display it. If this checks out, CGI is working.
So the first step thing to do is to use a wap emulator and get your index.pl file to display for you...but based on your comment that "The Page with the links for or to commands does show", this is already happening? (Otherwise, you wouldn't be getting that menu.) If this is the case, the page containing the menu is WAP content served with perl.
Once your server is configured to process the perl scripts and serve you wap content (which it appears to be), you can then start up the background daemon and try to get the iTunes stuff working. Given that the CGI is working, the only other thing that wouldn't be is your background daemon.
You are firing up the background daemon, and have verified that the file it expects to read ( /tmp/iTunesRemoteControl) does exist? If perl is rendering the menu for you, it should also be writing that file to the /tmp directory.
If I've misunderstood anything you've said, clear it up and let's go from there.