First of all, Let me tell you that the Broadcom kernel module is not yet stable enough to use it on daily basis ... So we'll have to disable the module and use ndiswrapper instead ... Ndiswrapper is a tool that will allow you to use the windows driver of your card.
One more thing; I believe that the ndiswrapper version shipped with Ubuntu is not functioning properly with the Broadcom drivers, so you'll have to manually download the latest version of ndiswrapper from here.
Inorder to disable the built-in kernel module you'll have to edit this file /etc/modprobe.d/blacklist and add the following line at the end of the file.

blacklist bcm43xx

Then Open a terminal and type the following:

# sudo -s
# rmmod bcm43xx
# rmmod ndiswrapper
# apt-get --remove ndiswrapper-utils
# apt-get install build-essential
# tar -xf /path/to/ndiswrapper-version.tar.gz
# cd /path/to/ndiswrapper-version
# make
# make install
# wget http://www.runithard.com/HOWTO-BCOM64WIRELESS/64-bit_Broadcom_54g_Drivers.zip
# unzip 64-bit_Broadcom_54g_Drivers.zip
# ndiswrapper -i netbc564.inf
# modprobe ndiswrapper
# apt-get install wireless-tools
# iwlist wlan0 scan
# iwconfig wlan0 essid "name-of-your-essid" #With the double quotes
# dhclient wlan0

I hope I helped.

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