mDNSResponder is used with Rendezous and is used for name discovery/reponses on a network that has other hosts using Rendezous. So, mDNSResponder isn't responsible for your normal DNS stuff. Are you sure now that you're in the DMZ you can access a DNS server? What does 'host www.gnu.org' tell you from a command line? What is listed in /etc/resolv.conf?
UNIX is simple and coherent, but it takes a true genius (or a programmer at any rate) to understand and appreciate its simplicity -- Dennis Ritchie