In 3.4e I right click it and then select other and fill in the info , wpa2 , password , automatic. This gets me connected .
I think the automatic can be changed to a specific type wpa2 or wpa1 type connection tkip or aes something not in SL right now. Is the wifi bcm43xx device mac adress 00: 11:22:33:44:55 type in the wifi router and or blocked in the wifi router / in allow list.
Might try wpa personal as enterprise has given me no connection in the past not sure why or if wpa enterprise is needed or what for.
Mine works from the live dvd 3.4e without needing anything else to be loaded.
Also as root in terminal:
This should list the signal strengh versus noise and if both is the same it would have difficulty connecting . Mine has to be for good speed / signal and least possible resend at least 20 difference 64 -> 84 and then it runs normal speeds , less work but but the internet becomes slower / laggy.
Iwconfig numbers is not fact but can give you a idea or using kwifimanager it should show signal strengh and it has a windows that can show noise versus signal.
Hope this helps.