You need to have at least one language set: Administration > Site administration > Site configuration > Languages tab
You need the login module enabled: Administration > Modules > Manage modules Make sure you enable “Login menu” not just “Login” The latter is the optional login block.
You need to set the correct menu access levels AND save it even if it looks right. Administration > Modules > Menus > Login menu
Having said all that, I can see the login OK on both your sites, so not sure why you are not. But perhaps this is not your “new site”?