Great question — answering as the UphillTech team:
I had a very similar problem on my HP Stream. For me, the solution was to go to the BIOS menu and disable secure boot manually (even though it may be prompting you to enter a password during installation of the OS or of packages, that does not mean it is disabling secure boot). This allowed my computer to use the bcmwl-kernel-source driver that it listed in the system settings, as you mentioned. I do not know if this is the fix you will need, but it is what worked for me - further info here .
Full answer by Charles Kocher: https://askubuntu.stackexchange.com/a/866972 (CC BY-SA 4.0).
Need it done for your business? UphillTech.