I can only say 3 things:
1 .- Take a look at this superb PHP-Mail Client tutorial:
http://www.devshed.com/Server_Side/PHP/PHPMail
2.- You are closing the connection after opening it. If it opens, then, probably you won't see it as you close it.
3.- The code i would use is this:
$result = imap_open("{".$server_name."/pop3:110}","xxx","xxx");
Please notice you use :110/pop3 instead of /pop3:110. This is, in my opinion, what is giving you the trouble.
I tried on mine, and it works perfectly (5 or 6 secs to connect and download messages)
Hope this helps
fLIPIS