I have this problem with my Lenovo IdeaPad Core17, Intel HD and Nvidia GT750M graphics card running a dual boot of Ubuntu 16.04 and Windows 10. On Windows everything works fine but on Ubuntu, HDMI isn't working for external monitors and I'm getting a black screen if I close the lid or suspend the laptop which forces a hard power off.
From question's revision #1:
First check the recommended nVidia drivers .
sudo ubuntu-drivers devices
Install the recommended driver, in my case, it were nvidia-418.
sudo apt-get install nvidia-418
Install nvidia-prime and nvidia-settings
sudo apt-get install nvidia-prime nvidia-settings
Reboot. You will probably get into a login loop.
If 4 above happens edit
/etc/default/gruband look for the line
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash nomodeset"
This was only necessary when installing Ubuntu. Now it's just causing your video drivers not to be loaded.
HDMI should work now. If the audio stops working, run
and then go to System Settings→Sound and set HDMI as default audio.
Links That helped me: