How have you determined the DNS server is not running ?
Below one displays the relevant daemons running listening on particular ports (to check if conflicting):
sudo netstat -nltup | grep "Proto\|:53 \|:80 \|:67 \|:471"
You shouldnt change Pi-hole's lighttpd port 80 TCP, or else Pi-hole wont be able to return a block page instead of an ad.
And if you cant change the port for Owncloud, adding a secondary IP address to the system could offer a solution if you bind the daemons to their particular IP addresses.
Some pointers in below posting on how to bind Pi-hole's dnsmasq and lighttpd daemons: