It works! I gave root read-only access to the /etc/bind/rndc.key file. I also changed some addresses in the /etc/dhcp3/dhcpd.conf file. I do not know which modification did the trick but I guess it was the access rights.
To be a bit more compliant to the Debian structure I moved the files in the /etc/bind/pz directory to /var/cache/bind.