Here's how to get real DNS set up on a Technicolor C2100T modem. This works at minimum when you're doing PPPoE (the usual method) on a C2100T modem sold or rented to you by Centurylink.
When you look up a nonexistent domain name, proper DNS service tells you it doesn't exist by returning Nonexistent Domain (NXDOMAIN).
In contrast, even on business lines, Centurylink's DNS service will snipe NXDOMAIN. Centurylink's servers (nameservers at 205.171.2.25
& 205.171.3.25
at least) return a Centurylink web server IP addresses when you should be getting NXDOMAIN.