I have 2 4311 broadcomes in house and each work flawless with ONLY 3.0.0-8.10 kernel installed.
So I know it works, very common wireless card.
No idea why it isn't working for you, perhaps other packages are missing.
Doubt it, they both worked out of the box for lite and gamers.
BUT, I do have a plan b now that 3.0.0-8.10 kernel is installed