Sharing the Internet connection over windows 7 requires one computer called the host that is connected to the Internet and to the rest of the computers on the internal network (LAN). Then the computers on the network connect to the Internet via the host computer. The host computer Internet connection can be wireless, modem (Ethernet or USB), 3G card or any similar device. To use ICS make sure that the LAN connection on each computer is configured to get an IP address automatically. This includes the LAN connection of the host computer.
Personally, I have never used the Windows Diagnostics Tool apart from the time when I decided to write a few lines about it. Most windows administrators would normally invoke other testing tools to troubleshoot network issues, however, for the less knowledgeable users the Windows Diagnostics Tool is an adequate solution that tries to automate the troubleshooting process. The tool button or link appears automatically when Internet Explorer cannot display a webpage.