Go to the command shell. Cmd.exe - type ping 127.0.0.1
If you get a response back then it's not your NIC (network interface card).
Then try to ping your gateway - ping <Gateway IP address>
If you get a response then your computer sees the gateway.
Before you do that though, try connecting directly to the router with an Ethernet cable and see if that works.
Maybe your not getting the needed drivers for the wireless NIC in safe mode.