Have you seen this page?

https://help.ubuntu.com/community/WifiDocs/Driver/bcm43xx#b43%20-%20Internet%20a\
ccess

Caveat: I have some vague recollections of trying it without success. I'll post
again if I can find my notes.

The reason there is not much current information and drivers is that
Broadcom has been supported directly (drivers included in the kernel) in
the last few versions of Ubuntu. This includes Lububtu since all the
'buntus use the same kernel. Which version (name or number) are you using?

Seen this?

linuxwireless.org/en/users/Drivers/b43#supported

Found my notes...

I've done a bit of exploration on a Dell Latitude D810, with a Broadcomm BCM4309
rev3. Not quite the same as yours, but close. I'm keeping it WinXP-only for
now, (small HDD), but I've tried some live CDs.

I've never gotten Wi-Fi to work on this machine with any *buntu, even with the
procedure I posted before (which claims it should work without a reboot).

However: Wi-Fi "just worked" when I booted a Fedora 15 Live CD. All I had to do
was enter my WPA key.

You might want to try a different lightweight distro.

If you find you have no success if getting this Broadcom device
working then apart from changing the version of Linux you can also
just change the Wi-Fi card to one that is supported ( Intel or Ralink
chipsets ). According to the diagrams on the HP support sites for this
laptop the Wi-Fi card lives beneath the keyboard and is a mini-pci
with the connections along the long edge. Not too difficult to get to
at all :-)

I had better luck with Mint LXDE, but I have more RAM. I also tried an USB Wi-Fi
card. PcLinuxOS LXDE may be a good choice, too.

I have never used Lunbuntu but. If you have a connection when
installing, The distro will likely find the driver to use upon installation.

When installing Ubuntu on others machines I would use a Wifi dongle
known by me to work. I can see that others claim Broadcom is supported
by the kernel but I never found that to be true. Because of Ubuntu
policies proprietary drivers haven't come on the ISOs I know of. This
does not mean that drivers are not made that work well, it only means
that Ubuntu in their wisdom didn't ever want it said that they broke
copyright law in an effort to supply the masses with a free system.

I don't believe Ubuntu will ever have to cave to MS for copyright issues
as long as you have to do some of the work. This compromise is well
worth it in my book, and one of the reasons I don't consider some of the
other distros like Mint.

If you have another connection other than Wifi, an update should find
your driver for you and offer an install of said driver.