I have a Broadcom card, and yours (BC4309) requires the b43 module.
From Linux Wireless Wiki: http://linuxwireless.org/en/users/Drivers/b43
b43legacy should be used on all BCM4301 cards and BCM4306 cards with a 80211 core revision of 4 or less. b43 should be used on all other cards.
There are a couple of things I always check with Broadcom on Netbooks and Laptops:
1. Physically switched on. Either by Button (laptop) or Fn+F2 (Netbook)
2. Check or reinstall everything related to wireless and kernel modules. It's amazing how somebody can't get Broadcom to work, just because they haven't got something as simple as wget installed!
What I would do (just a suggestion I might add, i'm sure you've probably tried this)
Connect the machine via cable into your router to get online.
sudo apt-get update && sudo apt-get upgrade
You'v probably got all these, but it won't hurt to check:
sudo apt-get install module-assistant wireless-tools firmware-b43-installer wget b43fwcutter
Module assistant will fetch everything needed to build, build-essential, kernel headers, libc etc.
Reboot.
Is b43 module loaded?
Let's reconfigure it anyway:
sudo dpkg-reconfigure firmware-b43-installer
It should go to openwrt, fetch (wget) and extract(b43fwcutter) the needed Broadcom firmware.
If your card is physically switched on/activated, we should be able to bring it up with:
And check:
I use manual (interfaces/resolv.conf) or wicd to connect (nm-applet and network-manager have caused me problems in the past), if you have wicd, make sure you have added wlan0 to the wireless part in configuration.
There have been some laptops/netbooks which played up, and needed to have the switch clicked and rebooted, or I had to remove the b43 module ad reload it, or take down and bring up wlan0 a couple of times, so go for a bit of trial and error. Your card uses b43, so if you have everything installed, and the b43 module loaded, it can only be a hardware problem after that.