BleepingComputer.com: Odd Issue with Internet Connectivity

Hi everyone, I'm having an odd issue with my 5 year old Sony Viao. I have my router connected to a Cable modem and the Sony computer is connected directly to the router via network cable. Sometimes I lose all connectivity on my Sony, but at the same time my laptop continues to work just fine in the house so I know its not the internet connection directly. I try powering down everything (including the computer, cable modem and router) and then sometimes I get good connectivity back for about 1/2 hour. Then what usually happens is after about 1/2 hour I start to lose connectivity on the Sony but only to web sites that I have not visited in the past half hour. So if I use google and CNN.com I can continue to use those sites, but when I try going to other sites that I didn't use during the 1/2 hour of good connectivity I get the standard "This page cannot be displayed message". Has anyone seen anything like this before, its really very confusing.

Thanks for everyone's help in advance.