That's a classic problem with PayPal IPN on many hosts. Something's preventing PayPal from telling your server that the order is completed, and thus the order number is never generated, nor is the confirmation email.
If you're on GoDaddy hosting, you'll have to make a coding change to fix a quirk resulting from a server change they made.
There are a bunch of troubleshooting steps mentioned here: http://www.zen-cart.com/wiki/index.php/PayPal