Networks

from within the router's configuration page, set the DNS to point to the resolved ip address of SSGROUP. Then on the client machines you should be able to use the automatic settings for both default gateway and the dns settings. This being contingent upon the fact that your Router is also the DHCP.
From within your Win7 machine, change your Network adapter settings back to the default settings then open an elevated command prompt and invoke the ipconfig /flushdns command and try again.
What you describe is most definitely an issue with DNS somewhere. If it is isolated to your laptop being the only node with problems then you should restrict your troubleshooting to it alone.
I presume you already have other Windows 7 machines attached to the network without any sharing problems. If that is not the case, then you are probably not aware of the fact that Win7 doesn't necessarily play nice with earlier versions of Windows in that area.

If client name resolution only works with the Win2000 Server's IP as DNS then that server is acting as your DNS server. Unless it's also a proxy server you should find that leaving the server's IP as DNS and using the router's IP as default gateway works for both Internet and name resolution. If the Internet still doesn't work with that configuration it means your Win2000 DNS server doesn't know how to find addresses of web sites out on the Internet. If that's the case Google 'DNS forwarder'.

This is usually DNS issues when names are not resolved. Either update the DNS or remove the machine from domain and update again. In case still further problem the check you IP address series.

Or is it completly static? If DHCP check that it's pointing to the aforementioned replies.