This post is in regards to a system that is not dual booting Windows OS and has Secure Boot disabled:
I can understand reticence to take actions you are uncertain about. One of the reasons we ask for help and for guidance is to gain that knowledge and certainty.
And you may need to downgrade the kernel, rather than upgrade it. Would need to know more before determining which you need...
If you installed the Open Source driver from post three, you may need to ensure that the existing Broadcom Proprietary driver does not conflict with it by blacklisting it.
echo -e "blacklist bcma\nblacklist brcmsmac" | sudo tee /etc/modprobe.d/blacklist-broadcom.conf
With that blacklisted, you must update initramfs:
sudo update-initramfs -u
You will not see a change until reboot.
Another step: Disable power management of Networking from disabling the card:
sudo nano /etc/NetworkManager/conf.d/default-wifi-powersave-on.conf
You will see:
[connection]
wifi.powersave = 3
Change that value to 2 to disable power management of networking:
[connection]
wifi.powersave = 2
Tap ctl+o to overwrite, then enter key to save current configuration. Tap ctl+x to exit the editor.
This too, needs a reboot to see the change.
Both of these are worth trying before trying to change the kernel.