Thank for the reply!
Sorry that I was unclear about this; I DO NOT have problems with the hardware - at least this is what I guess. The broadcom card is recognized by the NetworkManager and is reported as working, because kmod-wl and akmod-wl etc. are installed already (I do use the x86_64 kernel, not PAE)
I have problems CONNECTING BY WPA. The connection to any access point (at home and e.g. at my university) does not work. With my old notebook (using f13 i686) and other wireless hardware it worked. Also with an other notebook running ubuntu it still works. But with my new notebook (DELL studio) it DOES NOT work TO CONNECT to WPA access point. I've tested it on ubuntu also yesterday with the same result. It CAN USE the hardware, but fails to establish a connection...
I've found other threads issueing this, but most of them are from 2008 or even older and concern only fedora releases up to f12... So I'm am running out of ideas.... (may be I've have to use other 'strange' configs like ndiswrapper or else, but I prefer to use NetworkManager, if there is any chance...