I too was having this problem, and I think I just solved it.
The instructions state that we enter the “Mail Server”. Thus, I have been entering the name of the server that I enter into my browser when getting in for “Web Mail”. E.g.: email.yourdomain.com
When I did this, the wp-mail.php reports that there are no messages. Thus, I thought I entered the correct server name.
So, after beating my head against a wall for 2 days (and half a fifth of bourbon) I happened to see instructions that said we should enter “Incoming Server” and I thought that strange.
I went back into wp-admin, settings, writing… and changed the mail server field to reflect the “Incoming (POP3) Server” value. For GoDaddy, that is: pop.secureserver.net
BAM! It is now pulling email into WordPress!
If anyone from WP is listening… please make the instructions more clear! I suspect that a lot of people are making this same rookie mistake!