If pinging an external site by name works, I am thinking you can safely assume DNS is not the issue.is that a valid conclusion?
In an elevated CMD window, type ipconfig /flushdns which will clear the DNS cache on the server. Did that change things?
did you try to use the browser with an ip number?Could you suggest an IP address I can try this with, ones I have tried in the browser fail to respond
After laptop is connected do ipconfig /all from CMD prompt to find the information for your server static ip.