Assuming you can access websites with a browser, the phone is accessing the internet, so the only thing left is the setup of the email account. If you set it up manually, you did something wrong. If you let it set up automatically, delete that email account (
not your Google account - your gmail account if that's what you're using) and add a new account, then let it set up again. The only other possibility is that the email app is bad - install something like
K-9 Mail to see if that's the case.