Welcome to LQ!
Since you have a 4311, you should be using the 32 bit Broadcom driver from here
. If this is the one you have been trying to use, could you fill in some details about what seems to be going wrong. I've been using this driver with Slackware 12.2 on a Dell Mini, so I know it does work.
The readme file tells me to rmmod ssb b44 and a few others but this causes my eth0 adapter to quit as well:
02:00.0 Ethernet controller: Broadcom Corporation BCM4401-B0 100Base-TX (rev 02)
Kernel driver in use: b44
Kernel modules: b44
I'm guess that the readme file is telling you to rmmod the b43 driver, not b44. The b43 driver is the reverse-engineered wireless driver for many Broadcom wireless chipsets, but for the 4311, the official driver I linked to above is almost certain to work better. The b44 driver should not interfere with any of the wireless drivers, so you don't have to remove it.