Sorry but I was out for a while
Broadcom card 4312 is working just perfect with b43-firmware! Try just to reinstall it by synaptic and reboot your computer that should help.
Plese show "dmesg | grep b43" and "lsmod | grep b43" for sure module b43 is not load maybe because ssb module (there was some bug before - don't remember now exactly...)... so you can try "modprobe -r b43" and "modprobe -r ssb" and than just load b43 "modprobe 43" than check how it's work (if it's work...)...
"dkms-broadcom-wl" is loading b43 module to new installed kernel but I load it after upgrade kernel so didn't see reason to keep it... if someone updating kernel than it's good to install it (if see some reason - personaly I don't like dkms
Tex you're right I removed a lot of things but not firmware for wireless card. I didn't see reason to keep on cd modules like: bcm43xx, b43-fwcutter, etc... bcm we don't using any more as I know (it was for older kernels...) and fwucutter is software to extract firmware for broadcom card - just my opinion...