AppStore says my account is locked. But I can log in anywhere else

An account can just be locked for downloading content, you won't automatically be stopped from using the account everywhere else. Try resetting its password (and then logging out and back in everywhere) : If your Apple ID has been locked - Apple Support

If that doesn't fix it contact iTunes Support and see if they can/will re-enable it : http://www.apple.com/support/itunes/ww or https://www.apple.com/emea/support/itunes/contact.html