I realise that this is marked as solved but I have been struggling with a 2006 (Celeron M based) laptop with Broadcom BCM4311 wireless. No wireless with LL3.2 though worked with Vista. "Install drivers" seems to install proprietary Broadcom driver, but then I get not only no wireless but also no Ethernet! Also error messages on boot, the significant bit seeming to be
wl: module verification failed: signature and/or required key missing - tainting kernel
The offending module was removed by using Add/remove software, searching for BCM4311 and uninstalling it. Ethernet then worked again.
Searching this forum and elsewhere indicates many similar problems with B43 series chips historically, though mine may be due to the repository not using an up-to-date checksum method (see Jerry's post
https://www.linuxliteos.com/forums/on-topic/repository-server-upgraded/msg27566/#msg27566)
Anyway, I've switched to using a mini-dongle (Ralink MT7601U based, under £12) which works fine and gives b/g/n wireless rather than just b/g for the built in chip.
Hope that helps someone.