You should be signing in with the ID you use to sign into iCloud, not its email address.
If you still have the same issue, try entering the birthday one day earliert if you are not in the USA (time zone difference). Failing that, you will need to contact Support.
To contact Support: if you currently happen to have AppleCare, either because you recently bought Apple hardware or have paid to extend the inititial period, you can contact them here:
http://www.apple.com/support/icloud/contact/
You will need the serial number of the covered hardware.
If you are not covered by AppleCare, then - in common with other free email services - there is no free support (MobileMe Support is no longer available) and you will probably be asked to pay a fee - you could try asking them to handle it free, sometimes they do.