Laptop can't connect to the internet unless it's connected to an Ethernet cable

I've been having a problem for the last few weeks where my laptop wasn't recognizing my internet. When it stopped working I could see my connection through the network access, but it always failed to connect and the troubleshooter told me to restart my router. After trying a few times, shutting down and restarting my computer, doing a system restore, and a factory reset twice, I can connect to the internet through an Ethernet cable. However, now my laptop can't even see that any connections are available.

There are other computer in my house, all they all connect just fine. What should I do?
 
The laptops internal WIFI card has probably failed. You can get around it by using an external USB wifi adapter
 
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