09:00.0 Ethernet controller: Broadcom Corporation NetXtreme BCM5755M Gigabit EthernetPCI Express (rev 02)
I'm pretty sure that this is your wired card not your wireless... (sorry if you already knew that).
My suggestion is to try Sabayon. Evidently the folks at Sabayon don't care about silly legal issues because Broadcom 43xx cards work great with Sabayon and no fiddling around with firmware is required. Guess how I know?
I bet Puppy Linux works too.
Wireless support is a big reason I use the distros I do....