Is the Samsung NC10 running XP or Win7 Starter? If it is Win7 Starter, it wouldn't by default use MSHOME as its Workgroup name and this would have to be changed.
The error message about not having permission and having to contact the Administrator is a generic one which Windows regurgitates whenever a networked computer cannot be accessed. It is unhelpful and usually misleading. Make sure that folders you want to have available over the network have been "shared" properly and that any firewall software has been configured correctly (disabling isn't always sufficient, as background processes can still be running).
>>> The new windows 7 laptop diagnostics say "The DNS server isn't responding."
You could try using fixed DNS Server addresses. Use the Router's IP address as the "Preferred" address and one of your ISP's DNS addresses as the "Alternate" one.