There is more than one Software "Center". I'm seeing that some people have problems with certain ones. Since you say Gnome Software Center isn't working for you, then you can install
ubuntu-software-center. You can do this by running these commands from the terminal.
(Please note, the $ symbol is the terminal prompt. The command is what following the prompt.)
$ sudo apt-get update
$ sudo apt-get upgrade
$ sudo apt-get install ubuntu-software
You can decide which one will be your default by right clicking on a
*.deb package and choosing the one that works best. Then click on
Set as Default.
gnome-software are the same on Ubuntu 16.04.
ubuntu-software is a symbolic link to
gnome-software. If one is broken it's unlikely the other will work.
The system updates above may resolve the issue. If they don't, install an alternate software installer:
$ sudo apt-get install software-center
Perform these steps to fix
Rename or remove the
~/.local/share/gnome-software. In the steps below it's removed and will be recreated when you start
gnome-software. It currently has a list of what has been installed.
The first line will ensure the locked up instances are removed from memory. It might not be necessary.
$ killall gnome-software
$ rm -r ~/.local/share/gnome-software
gnome-software from the Unity Launch Button.