I don't know HOW to do it, cuz I've never bothered, but I know you can setup the GMAIL app to poll your other email addresses (POP3 included) and then push that email to your phone, via the gmail app. It polls the email addresses based on how frequently they get email, which saves you battery life.
Are you using the default mail program? I use K-9 mail for my earthlink account and it works just fine. I haven't used the default mail app in a while, nbut I remember it working for me when I did. The settings I see above are the same settings i'm using so i'm not sure where the disconnect it. I'm assuming you don't have any other connection issue? you can get to the net ok, browse the facebook app or whatever ?
K-9 Mail is another email program. You can get it from the market. Its the one I use and it works well. Give it a shot and see if you can get it to work for you. I use my earthlink account with it because it behaves better then the default one and has more options.