Ubuntu – Can’t view Wifi networks after upgrading to Ubuntu 16.04

I can't view any wifi networks after upgrading to Ubuntu 16.04 from 14.04. This issue also occurred when trying to upgrade to Ubuntu 15.10. This is what my network window looks like:

I have Broadcom enabled in the Software & Updates window:

Also there is no option for Wifi in the dropdown menu in the top right. The screenshots are from Ubuntu GNOME, but it also doesn't work for standard Ubuntu. How can I enable wifi networks?

Output of lspci -knn | grep Net -A2:

07:00.0 Network controller [0280]: Broadcom Corporation BCM43142 802.11b/g/n [14e4:4365] (rev 01)
    Subsystem: XAVi Technologies Corp. BCM43142 802.11b/g/n [1b9a:3002]
    Kernel modules: bcma, wl

Output of sudo apt-get install bcmwl-kernel-source:

Reading package lists... Done
Building dependency tree       
Reading state information... Done
bcmwl-kernel-source is already the newest version (6.30.223.248+bdcom-0ubuntu8).
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

Output of sudo apt-get install --reinstall bcmwl-kernel-source:

Reading package lists... Done
Building dependency tree       
Reading state information... Done
0 upgraded, 0 newly installed, 1 reinstalled, 0 to remove and 0 not upgraded.
Need to get 0 B/1,515 kB of archives.
After this operation, 0 B of additional disk space will be used.
(Reading database ... 153417 files and directories currently installed.)
Preparing to unpack .../bcmwl-kernel-source_6.30.223.248+bdcom-0ubuntu8_amd64.deb ...
Removing all DKMS Modules
Done.
Unpacking bcmwl-kernel-source (6.30.223.248+bdcom-0ubuntu8) over (6.30.223.248+bdcom-0ubuntu8) ...
Setting up bcmwl-kernel-source (6.30.223.248+bdcom-0ubuntu8) ...
Loading new bcmwl-6.30.223.248+bdcom DKMS files...
Building only for 4.4.0-21-generic
Building for architecture x86_64
Building initial module for 4.4.0-21-generic
Done.

wl:
Running module version sanity check.
 - Original module
   - No original module exists within this kernel
 - Installation
   - Installing to /lib/modules/4.4.0-21-generic/updates/dkms/

depmod....

DKMS: install completed.
modprobe: ERROR: could not insert 'wl': Required key not available
update-initramfs: deferring update (trigger activated)
Processing triggers for initramfs-tools (0.122ubuntu8) ...
update-initramfs: Generating /boot/initrd.img-4.4.0-21-generic

Output of sudo modprobe wl:

modprobe: ERROR: could not insert 'wl': Required key not available