Back. I have to sleep sometimes
It was just one of those times
From those pictures, it seems that DNS isnt setup properly.
Lets test that out.
On first system (the one trying to connect) go Start > Run. Type CMD. Then type ping
www.google.com
If that gives you error, than type ping 66.102.7.104. If that doesn't work, you have no connectivity. And it's not DNS issue.
( I assume here that you already enabled sharing on server)