Connect your notebook directly(ethernet), and use that connection to update your drivers, following the instructions in the linked forum page:
Broadcom wifi issue on 14.04 Lubuntu
Amended:
in response to a comment by @chili555, this link documents possible alternatives.
Excerpt from source:
Ndiswrapper is a Linux module which allows Ubuntu to use the Windows driver for wireless cards. One may want to use ndiswrapper for a number of reasons:
1) No open source driver provided in the Ubuntu repositories.
2) The driver provided by default in Ubuntu is not working out.
3) The proprietary driver provided by the card vendor is not working out.
4) Test ndiswrapper performance versus alternative driver(s).
5) Test hardware failure for your card.
The instructions listed through the link are clear and concise, and should be able to point you in the right direction.