The only known way to get this device working is ndiswrapper. ndiswrapper is a driver wrapper that only works with Windows XP drivers; Vista, 7 or 8 will not work. Please obtain a temporary wired ethernet connection and we'll install the ndiswrapper suite. Open a terminal and do:

sudo apt-get install ndiswrapper-common ndiswrapper-utils-1.9

Since yours is an older machine, I will assume it is a 32-bit machine; confirm:

arch

If it returns 'i686,' then yours is a 32-bit install and we'll proceed. If not, stop and tell us and we'll change a thing or two. Download this file to your desktop: https://dl.dropboxusercontent.com/u/58267392/Broadcom_bcm43xx_USB_32_64bit_v2_amended.zip (from my personal Dropbox). Right-click it and select 'Extract Here.' Back to the terminal:

cd ~/Desktop/Broadcom

Press Tab and the remainder of the file name will fill in automagically; press Enter.

sudo ndiswrapper -i bcmn43xx32.inf

Now check the install:

ndiswrapper -l

It ought to report: bcmn43xx32 : driver installed
device (050D:615A) present

sudo depmod -a

sudo modprobe ndiswrapper

If there are any errors, post them and we'll do our best to sort them out.

In some cases,even though you installed ndiswrapper from Ubuntu sources, it doesn't install properly; the remedy is to download and compile it yourself. Please get a temporary wired ethernet connection and do:

sudo apt-get install linux-headers-generic build-essential

Now download this file to your desktop: http://downloads.sourceforge.net/project/ndiswrapper/stable/ndiswrapper-1.59.tar.gz Right-click it and select 'Extract Here.' Then do:

cd ~/Desktop/ndiswrapper-1.59

make

sudo make install

sudo modprobe ndiswrapper

If the device is not working as expected, look for clues here:

dmesg | grep ndis

If the output is extensive, post the result here and give us the link in your reply: http://paste.ubuntu.com/

To get the module to load on boot, open a terminal and do:

sudo -i

echo ndiswrapper >> /etc/modules

exit

You should be all set.