Why can't I connect to WiFi?

I can't connect to our wifi. After I click to connect to our WiFi, it takes me to another window. The URL says apple.com and the title of the page is Log In, but the page shows up blank with just an odd line of code at the top. It looks like this.

http://puu.sh/iZLdh/c8415d76c1.jpg

After that the WiFi connection ceases.

The wifi itself is working fine, my sister is using it without problems on her laptop currently so no resetting of the router is needed.

I've restarted the device and reset the network information.

I'm entering the password right.

I'm currently wiping the device clean.

Apple Customer Service was about as stupid as a pile of rocks. "Herrderr it's your WiFi that's the problem because if you wiped it clean it can't be a software issue."