Cannot connect to some websites....help

Hello,

I am not computer savvy by any means, but I need help trying to figure out why our new modem wont connect to some websites that I could with our old router. We had to get a new modem from Qwest last month and ever since that time there are some gamming websites like king.com and worldwinner that says the DNS is incorrect, or does not exist. If I look up the website under cached it brings it up. So it has to be an issue with the DNS.......what is this, and how can I fix it.......thanks