Install the NVIDIA drivers and NVIDIA Optimus (PRIME) in a different way :
1. Remove all NVIDIA software you tried to install before.
Highlight the Ubuntu menu entry and press the E key.
Add nouveau.modeset=0 to the end of the linux line.
Press the F10 key to boot into the Ubuntu system.
When the login screen appears press Ctrl+Alt+F1.
Enter your user name and password ... then execute :
sudo apt-get purge nvidia*
sudo reboot
2. Install NVIDIA drivers 352 from the Ubuntu repositories.
Highlight the Ubuntu menu entry and press the E key.
Add nouveau.modeset=0 to the end of the linux line.
Press the F10 key to boot into the Ubuntu system.
When the login screen appears press Ctrl+Alt+F1.
Enter your user name and password ... then execute :
sudo apt-get update
sudo apt-get install nvidia-352 nvidia-prime
sudo reboot
Update addressing your feedback that it still doesn't work with drivers 352 :
1. Remove the currently installed NVIDIA 352 drivers.
Highlight the Ubuntu menu entry and press the E key.
Add nouveau.modeset=0 to the end of the linux line.
Press the F10 key to boot into the Ubuntu system.
When the login screen appears press Ctrl+Alt+F1.
Enter your user name and password ... then execute :
sudo apt-get purge nvidia*
sudo reboot
2. Install the latest official stable NVIDIA 361 drivers.
Highlight the Ubuntu menu entry and press the E key.
Add nouveau.modeset=0 to the end of the linux line.
Press the F10 key to boot into the Ubuntu system.
When the login screen appears press Ctrl+Alt+F1.
Enter your user name and password ... then execute :
sudo add-apt-repository ppa:graphics-drivers/ppa
sudo apt-get update
sudo apt-get install nvidia-361 nvidia-prime
sudo reboot