Why is named the owner of / and /root? Is this something you did? It is very suspect. Check the named (bind) packages for bugs. If you don't find one regarding / and /root's ownership changing to named, you may have been rooted, and should reinstall from scratch (without installing bind). If you are in fact a newbie, why are you running named? I would suggest you uninstall bind until you are more able to administer it, but that is outside this question.
To fix your problem:
chown root:root /
chown root:root /root
chmod 644 /root/.dmrc
Also, I would STRONGLY suggest you NEVER log into a GUI as root. The fact that you may have a broken name server means it would be quite easy to root your box if you are logged in as root and open any webpage.