Software Center won't open at all

I was also facing this same problem; I followed these steps to fixed it:-

To uninstall Software Center:

sudo apt-get remove software-center
sudo apt-get autoremove software-center

To re-install Software Center:

sudo apt-get update
sudo apt-get install software-center

Thank you Mohamed Slama for askubuntu.com/a/133473/464430

Similar problem happened to me after I installed 16.04.1 LTS and updated software with Software Updater in it. When I tried to install new software from *.deb file, the Ubuntu Software opened and then exited quickly. I found the answer here. Actually I just tried to

sudo apt-get update

in terminal. Then Ubuntu Software worked. I don't know why.

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

Then it should enable to open software-center from dash or with gnome-software from terminal.

Ref: here