I may open dmesg in nano and change the disabled netlink to enabled and then restart the PC with the ethernet from the router connected.
That won't change anything. Dmesg is just a log file of the messages that are sent by the kernel during operation. For instance enter dmesg | tail and it will show you the last few messages, then plug in a usb device of some kind wait a little ( 15 seconds or so) and run dmesg | tail again and it will show you just what the kernel reported when you plugged in the device and what it did with it.
So so far we have not discovered anything by looking at the log files. That is not all that uncommon but keep looking. Did you enable boot logging?
Try this command lspci -vv and find the section related to your broadcom cards and post it please. -vv will show alot of other information about the hardware and what the kernel loaded for them.
Stay with your google searches and keep reading. Some times your brain will put the info from several unrelated places together and lead you to the solution
On more that one occasion that is how I ended up solving my problems.