Linux has it's problems with Broadcom drivers, I myself have a Lenovo laptop with the same wireless adapter and always have to manually install the drivers on any Linux distribution.
On Ubuntu the easiest way is to install the proprietary driver since the kernel integrated opensource drivers do not work with this card.
Firstly you have to get internet access on the device in any other way, be it through an ethernet cable or for example an android device. You can connect your phone to your WiFi and usb tether the connection to your laptop.
Next open the Additional drivers program from the Dash app launcher and look for the Broadcom wireless adapter (I am currently not on my ubuntu machine so I cannot check the exact text that will be shown, if anybody has the same card, free to comment and I'll edit the answer). Check the use proprietary driver checkbox and hit apply. It will take a few minutes and your driver will be installed. You might have to reboot to get apply the changes