I'm not aware of CUPS directly interacting with the DNS settings, but here's some things to check:
/etc/resolv.conf should have your domain name servers listed (unless you're using DHCP).
You should be able to ping certain web sites by their name. Some won't allow ICPM requests, but even if they don't, you should see the resolved IP address in the second line of ping's output.
Try a different browser.
Did you try disabling CUPS before you installed a new user? "/etc/rc.d/rc.cups stop" will stop CUPS and if you "chmod -x /etc/rc.d/rc.cups" it won't start at startup (chmod +x to get it back).
Beyond that, I don't have any ideas without more specific information. (dialup or direct, and what's the results of the above solutions)