And conversely, I have a paid developer account and it would not let me in. I think it might be confused because my Apple ID is an old-school one that isn't an email address.
Access to technical resources such as pre-release software and associated documentation, and information related to distributing iOS or Mac apps on the App Store are benefits offered to Apple Developer Program members.
Either the Apple ID and password you entered is not associated with an Apple Developer Program, or the Program that you are enrolled in does not have access to this resource.
I have a free developer account and was able to log in. I don't have a @me.com address so I couldn't check Mail, but the rest worked.