boot - Installing latest Nvidia from Xorg PPA gives black screen

After several years of using dual boot (windows to play and Ubuntu to work) I decided to just use ubuntu, but I have a problem after installing nvidia-drivers 331.20 and rebooting the screen is black, I have seen many solutions for this problem, in particular I have run the following command sudo apt-get purge nvidia* then sudo reboot after which I am ready to use ubuntu.

How can I fix this problem since I really want to play but the latest drivers (331.20) are the ones that are optimized for the 700 series.

I am pretty sure you might be suffering from the same ordeal I had to experience when I was using the Xorg PPA (I am guessing you are using that PPA as well). If you are, this is the first time this is happening with that PPA, in that, with the latest package builds (For 319, 331 and I could guess any other updated package build) they have merged the Bumblebee and Primus packages into one. So when you install any of the Nvidia-??? packages you are also installing the latest bumblebee and primus ones.

This is good in a sense that now you install 1 packages and it installs the drivers for either Hybrid systems or normal, common, one Nvidia to rule them all computers. The problem here is that the Bumblebee configuration files and blacklisting the Nvidia-??? modules, so you will get a horrible black screen upon rebooting.

If you ONLY have an Nvidia card, PCI-EX one like mentioned on your question and there is no hybrid system on that same computer (just in case) then I would suggest to do the following:

sudo apt-get purge bumblebee primus   
sudo rm -fr /etc/modprobe.d/bumblebee.conf
sudo reboot

This will remove the bumblebee packages which you don't need for that system. It will then remove the blacklisting file that is creating all the mess. Lastly it will reboot the computer after which, your system should run just fine. This is all thanks to a finding by Tareeq in this Bug report. If this applies to you please let the Bug in launchpad know by clicking on the "Is this affecting you" message. If not then we can proceed with other ways of solving it.

I will also encourage you to read the Nvidia installation and configuration guide to shed some light on the problem: How do I install the Nvidia drivers? and possible solutions