You also have to install linux headers. I hope you are able to connect via ethernet to do this? This is for the current kernel.
sudo pacman -S linux-headers
I apologize if i have caused you any problem here. I forget that not everyone sees the info on the wiki and assume they know that the headers are needed also.
I usually install the headers again and reboot. Or as @ringo say’s sudo mkinitcpio -P after. It should work if the Broadcom driver currently works. If you are able to give it another try installing broadcom-wl-dkms and then install linux-headers and reboot and see. I have this Broadcom chip running on mine and that’s how i install it and it works no problem.
03:00.0 Network controller: Broadcom Inc. and subsidiaries BCM4360 802.11ac Wireless Network Adapter (rev 03)