That's what Forums are about, learn something, possibly help someone else with the same sort of problem.
I need to explain a bit about Fedora before we start. Its philosophy is to have the newest, 'bleeding edge', software versions that are available.
Thus when Fedora 8 came out it had the very new b43 kernel driver/module in place of the bcm43xx, that was the first time my broadcom 4318 card in this laptop worked reliably without recourse to ndiswrapper.
However, my broadcom 4306 card in another machine still wouldn't.
Then in an update 3 or 4 weeks ago I noticed there was an updated b43 package. I tried that and my 4306 now works.
I don't have a 4311 to try so I can't say which of the versions of the b43 will bring it to life, just that one of them should.
My first advice to anyone doing this would normally be to update their machine using the wired connection if possible. However, Fedoras bleeding edge philosophy has gone a step to far at the minute and if you upgraded you would get a new kernel which has caused a lot of trouble in the networking area for some people.
I suggest that we try this with what you have installed, bearing in mind that it may not work and hoping that by the time we have got that far there will be a new Fedora kernel to upgrade to.
What you need to do for this card is to download this file:
you'll probably just be able to click on the link, or copy and paste it into your browser address bar.
Store the file in a folder somewhere.
cd (change directory) into that folder and issue the command:
tar xjf broadcom-wl-188.8.131.52.tar.bz2
to un-tar it.
cd into the new folder and then specifically into the kmod folder within that.
Issue the command:
that's a space and a minus sign after the su. It gives you full root rights together with roots full environment.
From that root command prompt:
b43-fwcutter -w /lib/firmware wl_apsta.o
This cuts the firmware the card will use from the downloaded file and installs it where the b43 driver will look for it.
If you have NetworkManager running, you will have a networking icon on the top Gnome panel in the notification area to the right. That is what you will use to control the card.
If it is not there, from your root command prompt again:
or Gnome system menu - administration - services, it gets you the same tool. Look for NetworkManager, put a tick against it, Start it from the toolbar and Save the configuration so it starts at boot time.
With luck, when you now reboot you will be able to left click on NetworkManager and see a list of wireless networks to select from.
Try it out and post back with questions either before or after the process.
EDIT Apologies apeace if you read this. In my hurry the other evening I pasted the wrong link to the firmware package. I've amended it now.