If low battery charge is not the issue (which it may well be, based on Your description), one thing that may fix Your issue would be to try a newer kernel version.
Upgrading Your kernel may seem difficult, but it is actually fairly straight forward, provided that there are newer versions packaged and available (which is almost always the case).
To check Your current kernel version, open up a Terminal enter the following command:
uname -a
The output will look similar to this:
Linux {hostname removed} 4.5.2-040502-generic #201604200335 SMP Wed Apr 20 07:37:26 UTC 2016 x86_64 x86_64 x86_64 GNU/Linux
As You can see here, in my case I have chosen to upgrade to kernel version 4.5.
Here is a guide that explains how to do this in more detail: http://ubuntuhandbook.org/index.php/2016/03/upgrade-linux-kernel-4-5-ubuntu/
Note: If You still experience issues, it could also be worth while to try uninstalling/removing the firmware mentioned in the other question that You originally linked to, as it may not be needed at all. I would suggest that You try experimenting with this.
Update:
I just stumbled upon this answer that may also help You out: Drivers for Broadcom BCM43142 on Ubuntu 14.04 (Trusty Tahr)