Why does me.com always redirect to Find My iPhone?
It's likely that you migrated your MobileMe email to iCloud and you can only log into http://me.com to access the few things that remain. So, try getting your mail at https://www.icloud.com/

If you didn't migrate things, you may have to open a support ticket with Apple to have them look at your account. You can always try logging into the same URL from a new computer or clear cookies, caches in the browser in case it's something that isn't clean on the client side, but in all likelihood, the problem is on the server end and the application on the web server believes you don't have mail any more for your logged in account.