Wireless card is recognized but stopped forming connections

Question

OS Ubuntu 16.04, Cinnamon desktop

Laptop HP Pavilion 15z

NIC Broadcom BCM43142 Wireless

driver bcmwl-kernel-source

kernel 4.10.0-33-generic

This is an existing installation on which wireless used to work painlessly. Now, the card is recognized, and the driver is installed, but the OS will not even attempt to form a wireless connection. There is no option for "Wireless" in the taskbar's networking applet, and the symbol is the "No connection" one.

sudo service network-manager restart does nothing.

sudo lshw -c network gives

*-network UNCLAIMED
    description: Network controller
    product: BCM43142 802.11b/g/n
    vendor: Broadcom Corporation
    physical id: 0
    bus info: pci@0000:02:00.0
    version: 01
    width: 64 bits
    clock: 33MHz
    capabilities: pm msi pciexpress cap_list
    configuration: latency=0
    resources: memory:fea00000-fea07fff

lspci gives

02:00.0 Network controller: Broadcom Corporation BCM43142 802.11b/g/n (rev 01)

Under Menu > Preferences > Additional Drivers, there is an entry for

Broadcom Corporation: BCM43142 802.11b/g/n
This device is using an alternative driver
(*) Using Broadcom 802.11 Linux STA wireless driver source from bcmwl-kernel-source (proprietary)
( ) Do not use the device

apt-cache policy confirms the driver is installed:

$ apt-cache policy bcmwl-kernel-source
bcmwl-kernel-source:
    Installed: 6.30.223.271+bdcom-0ubuntu1~1.1
    Candidate: 6.30.223.271+bdcom-0ubuntu1~1.1
    Version table:
   *** 6.30.223.271+bdcom-0ubuntu1~1.1 500
          500 http://us.archive.ubuntu.com/ubuntu xenial-updates/restricted amd64 Packages
          100 /var/lib/dpkg/status
       6.30.223.248+bdcom-0ubuntu8 500
          500 http://us.archive.ubuntu.com/ubuntu xenial/restricted amd64 Packages

However, the driver module does not appear to be loaded:

$ sudo lsmod | egrep bcmwl
$

If I try to load it:

$ sudo modprobe -n bcmwl-kernel-source
modprobe: FATAL: Module bcmwl-kernel-source not found in directory /lib/modules/4.10.0-33-generic

Indeed, there is no trace at all of bcmwl in the directory /lib/modules/:

/lib/modules$ find . -name "*bcmwl*"
/lib/modules$ grep "bcmwl" ./*
/lib/modules$

I've already exceeded my understanding of the situation, and I have no idea what to do next. Please help.

Edit Apparently the module is named wl.

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

According to this page, it's a UEFI Secure Boot problem. When I removed the laptop battery to fix a problem last night, Secure Boot re-enabled itself. After entering BIOS to disable it again, wireless now works.