I’m also at goDaddy (shared server). I have debugged the problem up to the point where the fsockopen in class-pop3.php times out without establishing a connection to goDaddy’s POP server.
After three emails to the goDaddy support desk, the best answer I could get from them is:
Unfortunately we do not allow outgoing connections through port 110 from our shared hosting environment.
Please post a reply here if you could convince goDaddy to change their policy.