When you go to the connection icon, do you see (underneath "Connected to xxxxx") the words 'internet access' or 'no internet access'? That might give us a clue as to what the problem is.
However there are usually two main reasons why you could find that you can't connect to the internet. The first, as GM suggests, is that your router isn't connecting to the internet (even though it's connecting to your computer). That can usually be fixed simply by
completely unplugging it. (Disconnect the power. Disconnect from the phone line. Unplug any Ethernet cables). Then plug everything back in and try again.
The second (and possibly more likely, given your use of System Restore) is that you need to reset the TCP/IP stack. Don't worry, it's a lot easier than it sounds!
http://www.windows-secrets.co.uk/2013/08/repair-the-windows-87vista-tcpip-stack/