On my domain controller (Server 2008 RTM SP2), the firewall is on for Private and Public profile, but it is of for Domain Profile.
I'd like to turn it on, but when I click on Windows Firewall Properties in Server Manager, the Firewall state displays Off and is greyed out. It cannot be a permission problem, because I'm logged as the Domain Admin and I can change the settings for the Private and Public Profile.
What can be the reason for this, and how to turn on the firewall ?
Your firewall state is being managed by Group Policy. To change it, you need to change the group policy that's managing your server's firewall profiles.
On another note, if you don't really know what you're doing (and no offense, but you don't seem like you do), don't mess around with the firewall on domain controllers. You're just gonna cause yourself a lot of pain if you do.