I had similar experience where my ADSL provider does not seem to provide DNS info thru DHCP, I'm not sure it's because it's not possible in ADSL or simply just they don't do it.
But I managed to work out the solution, I've got the DNS server IP from the provider, unlike the IP, they are static most of the time, and inside the /etc/resolv.conf file, I put in the lines
NAMESERVER IP.OF.PRIMARY.NAMESERVER
NAMESERVER IP.OF.SECONDARY.NAMESERVER
Then everythings are fine.