16.04 Cannot install anything from Ubuntu Software center

If you want to install programs via .deb files, I suggest to use Gdebi.

It's a lightweight application that is better at installing .deb packages, and is quicker as well. If there are dependencies, it notifies that as well.

In the terminal, type:

sudo apt install gdebi

You can right click on .deb file and select to open it with Gdebi.

If you like Gdeb, you can make it default to have it open all the .deb files in future.

Read this: http://itsfoss.com/gdebi-default-ubuntu-software-center/

If you need to install software that is not in the repositories, and the Software Center is not working, there is an alternative but it requires the terminal. You must first navigate to the folder where you downloaded the debian package, which is usually in the 'Downloads' folder.

You can open the terminal from that folder by right-clicking and pressing "Open Terminal", or you can navigate to it via the Terminal by:

cd /path/to/folder

After that you just run this command:

sudo dpkg -i nameofpackage.deb