> > Device-1: Broadcom Limited BCM4313 802.11bgn Wireless Network Adapter > ok, this is your card.
Lets see output of $ iw dev [your_dev_name] it should be $ iw dev wlan0 I believe Also, try to ping your wifi router ip address and some Internet address like $ ping 8.8.8.8 Then, check https://www.speedtest.net/ : it gives a little bit more information than "fast.com"