What ISP are you with?
If you can access some websites but not others, it sounds as if your router settings for DNS are OK, but the problem is either with your hosts file or with your ISP.
Check the hosts file for contamination: C\windows\system32\drivers\etc\hosts - note no extension. It should have no entries ither than 127.0.0.1 = localhost, apart from comment lines.
Assuming that is clear, run ipconfig/displaydns and save it for reference. Now ping
www.microsoft.com - you should see:
Pinging lb1.
www.ms.akadns.net [207.46.193.254] with 32 bytes of data:
Although you won't get a response.
If you don't resolve the name to the IP address it is a DNS problem. If it resolves it incorrectly, try running ipconfig/flushdns and trying again.
SD