Something seems to be in conflict or something when it's connected to this router using 192.168.1.1.
You sure you don't have any other devices using 1.11?
One thing you can try, Disconnect ALL other devices accept for 1 wired PC and the DNS. Change the routers ip address to .0.1 temporarily. See if you can get the DNS working there. If you can, then go in and change the DNS to a static IP address of 192.168.1.20 and the gate way to 192.168.1.1. Save settings then power Down the DNS. Go back and change the routers IP address back to 192.168.1.1. Reboot the router and your PC and check that you can access the internet. Then power ON the DNS. Try accessing 192.168.1.20 after the DNS is ready.
What is the DHCP IP address pool set for on the DSL modem? 192.168.1.100 thru .200?