This is quite common with Windows 8. When on LAN you only have an IPv4 default gateway address, but on WiFi your first choice default gateway address is an IPv6 address.
See post 18 on this thread, you cannot have more than one active default gateway, this effectively means that you have no default gateway & hence the limited connectivity message:-
The solution is to disable IPv6 on that WiFi adapter. See this site for guidelines:-
Then please send me the ipconfig /all again, so I can check it.
That looks much better, you only have an IPv4 default gateway. However, obviously it still does not work, have a look at these suggestions or Google windows 8 limited connection:-