The problem is solved by putting in some specific domain name servers in the /etc/resolv.conf file other than the modem. That is not as easy as it appears because that file is automatically generated.
The script that generates that file is /sbin/dhclient-script and it is pretty easy to modify to do what we want. Just open it up in your favorite editor and add two lines (one if you do not count my comment):
Of course, you may have to fiddle around with the nameserver number and use something more appropriate for your connections. This will require some research on your part.
After this, open up network interface and adjust the DNS lookup to mirror resolv.conf. Just add the DNS servers you added in the script.