No HDMI output after upgrade to 16.04

I had the same problem. Nothing helped from the list of drivers from the nvidia and online terminal helps.
Ubuntu provides genuine drivers to your system after recognizing your hardware.
The solution....

1. System Settings => Software and Updates => Additional Drivers.
Select the first option in the list and apply changes. If that fails, try the other options from the list in "Additional Drivers".

Thanks for the suggestion Albert. I had no recommended additional drivers, so I went to Intel and found information about their Linux support (www.01.org). On that page they described what was being done and in the associated forum, stated that the i915 driver was already packaged with 16.04. (I edited my question to reflect this).

So I'm looking for a work-around that will get me going. Any suggestions?

Can you provide a SCREENSHOT/PICTURE of your "Additional Drivers".

http://i.stack.imgur.com/vbZOs.jpg

The image should look like this where recommended drivers are provided just for your hardware.

Clean up your installed graphics driver using...

sudo apt-get purge nvidia*
sudo reboot
Then try checking your "Additional Drivers" again.

Here is the screen shot: https://www.dropbox.com/s/t36g687mv82tjb1/Screenshot%20from%202016-11-10%2013-10-51.png?dl=0

The additional drivers did not change after the nvidia purge.

Try the following as one may work else am out of ideas..

1. sudo apt-get purge nvidia*
2. sudo apt-get install nvidia-current

Or select from the list provided under the code:
1. sudo apt-get purge nvidia*
2. sudo apt-cache search nvidia-[0-9]+$
3. sudo LIST SELECTION

FROM NVIDIA SITE, nvidia-340 should work for you as it did work for me too.
PS.

Hi again,
I have tried both of your suggestions. In each case there seems to be an installation of the nvidia drivers, but when Additional Drivers is opened, there are no radio buttons for choices. The same screen image is presented that I have already shared. Could there be something blocking?

Yes i believe linux have current drivers added to their packages.
I hope your system is updated... else try updating it by:

sudo apt-get update
Try the suggested solutions above.

or https://aboutsimon.com/blog/2016/07/20/Ubuntu-16.04-external-monitor-flickering-and-turning-off-on-intel-i915.html

Does your system detect your external monitor from "System Settings => Display"?

or download i915 driver/update/upgrade tool from:
www.01.org
https://wiki.archlinux.org/index.php/intel_graphics
https://wiki.archlinux.org/index.php/Xorg

Yes, Ubuntu 16.04 has the i915 drivers included. The Intel driver tool does nothing different and the i915 driver is not scheduled (at this time) for an update. So, what I've got is it.

As mentioned in my original request for help, I've upgraded from 14.04 and have made sure that the system is updated using both the terminal and the GUI. With the exception of some security updates, there seems to be nothing to address the video driver problem.

I've used all of the suggestions so far without a positive outcome, namely, the HDMI output is not going out to a monitor (of any kind; I've tried several). The HMDI is not being recognized when the display settings poll for other monitors. Following this thought, I looked for trouble with i915 and found that there is a bug report. But, if I loaded the nvidia drivers, shouldn't I get the choices I saw in you Additional Drivers screen? Why can't I use other drivers instead of the i915 from Intel ... despite the fact that I have an Intel card? Shouldn't I purge the i915 drivers?

I purged my drivers to exit endless loop at the login screen loop. And also to remove my installed nvidia driver.
After the purge, i thought my external blank monitor problem was a bug. Now i know its not a bug.
My "Display" found my monitor but the monitor was still black. So it was driver problem.
And yes you can install other drivers instead of i915. I installed "nvidia-current " which is nvidia-304, (my default driver) but i still had the black monitor screen. Then i installed nvidia-340 which solved my external monitor black screen problem.
The list of other drivers to try are under the code: sudo apt-cache search nvidia-[0-9]+$

I basically understand what you wrote and I believe that the nividia drivers are installed. I don't understand what can be done beyond what you have suggested and what I have done thus far. Unlike yours, my system is not finding my monitor. Should I try to force the driver; is that possible to do? Or, do I purge the i915 driver?

Yes you can purge your driver.
And forcing the drivers is possible but it will not make any difference in this case.
Could you try using different Kernel?

What is the output of "xrandr"?( Whiles connected to the external monitor?)
Output of "sudo lshw -C video"?

Before your post, I upgraded to the 4.5 kernel that resulted in no difference.

xrandr output is as follows:
Screen 0: minimum 8 x 8, current 1360 x 768, maximum 32767 x 32767
eDP1 connected primary 1360x768+0+0 (normal left inverted right x axis y axis) 256mm x 144mm
   1920x1080 60.00 + 59.93
   1680x1050 59.95 59.88
   1600x1024 60.17
   1400x1050 59.98
   1600x900 60.00
   1280x1024 60.02
   1440x900 59.89
   1280x960 60.00
   1368x768 60.00
   1360x768 59.80* 59.96
   1152x864 60.00
   1280x720 60.00
   1024x768 60.00
   1024x576 60.00
   960x540 60.00
   800x600 60.32 56.25
   864x486 60.00
   640x480 59.94
   720x405 60.00
   640x360 60.00
DP1 disconnected (normal left inverted right x axis y axis)
HDMI1 disconnected (normal left inverted right x axis y axis)
HDMI2 disconnected (normal left inverted right x axis y axis)
VIRTUAL1 disconnected (normal left inverted right x axis y axis)

sudo lshw -C video output is:
  *-display
       description: VGA compatible controller
       product: Haswell-ULT Integrated Graphics Controller
       vendor: Intel Corporation
       physical id: 2
       bus info: pci@0000:00:02.0
       version: 09
       width: 64 bits
       clock: 33MHz
       capabilities: msi pm vga_controller bus_master cap_list rom
       configuration: driver=i915 latency=0
       resources: irq:42 memory:f7800000-f7bfffff memory:e0000000-efffffff ioport:f000(size=64)

I hope you can see something.

Work around to force the signal to the display ports you are using, HDMI1.

http://askubuntu.com/questions/150879/can-i-force-vga-signal-output-even-when-xrandr-shows-disconnected

Using your suggestion and the URL you provided, I did the following:
xrandr --output eDP1 --mode 192x1080
xrandr --addmode HDMI2 192x1080
xrandr --output HDMI2 --mode 192x1080 --same-as eDP1

The result was:
xrandr: Configure crtc 1 failed

I tried it by unplugging the HDMI display and keeping it plugged in with the same results.

I also tried to purge/uninstall all Intel drivers, but when I use "lshw -c video" to see what is running, I still see the i915 driver in use:
  *-display
       description: VGA compatible controller
       product: Haswell-ULT Integrated Graphics Controller
       vendor: Intel Corporation
       physical id: 2
       bus info: pci@0000:00:02.0
       version: 09
       width: 64 bits
       clock: 33MHz
       capabilities: msi pm vga_controller bus_master cap_list rom
       configuration: driver=i915 latency=0
       resources: irq:42 memory:f7800000-f7bfffff memory:e0000000-efffffff ioport:f000(size=64)

I still think that something is forcing the use of the i915 driver and contrary to my best efforts, I can't get rid of it to use the nividia drivers. Any thoughts?

Your screen resolution is out of range and "lshw" list your specification of hardware devices which is why it still shows.
Try:
xrandr --addmode HDMI2 1920x1080
xrandr --output HDMI2 --mode 1920x1080 --right-of eDP1
or
replace "right-of eDP1" with "same-as eDP1". It could also be "left" or "above" as you know.

Am not sure what could be done for such an unresponsive driver from a working hardware.

I'm stumped too. So that I could use my large screen monitor, I bought a mini display port to HDMI adapter ... and it works great!

Why does the mini display port work and not the HDMI? I can't figure it out. And, I still can't figure out how I can "flush" the i915 driver!

I still want the HDMI connector to work. Is there anything else to check?

Good something works for now.
Have your output from "xrandr" changed?
And i don't know how to flash the driver.

xrandr shows the mini display port working as HDMI1, but HDMI2 is still showing "disconnected" and the mini HDMI port will not recognize the external monitor.

Regarding the driver, Intel has a Graphics Tool for Linux. I've loaded it and used to ensure that the Intel driver is correct and up-to-date. But, the nvidia drivers never show up. They are loaded and I can check them by using: dpkg -l | grep nvidia

Because I've been updating the nvidia driver is now the current 367.57 version. And, I have a nvidia GUI tool called: NVIDIA X Server Settings. It doesn't show much or give any hint on how to use it. It doesn't allow any changes that affect the HDMI output

I'm not sure what else can be done. I still think the nvidia drivers are being blocked or turned off somewhere.

Any thoughts?

I'm doing a lot of searching and I'm finding out that if I don't have a nvidia card, the software will not recommend drivers. It seems that some laptops have two video cards, one intel and the other nvidia. In those cases, the software recognizes the two cards and adds options to Additional Drivers. I'm thinking that since I have only an intel card, I'm not getting the options for other drivers. Here's the results I see:
tablet3@tablet3:~$ lspci -k | grep -A 2 -i "VGA"
00:02.0 VGA compatible controller: Intel Corporation Haswell-ULT Integrated Graphics Controller (rev 09)
 Subsystem: ASUSTeK Computer Inc. Haswell-ULT Integrated Graphics Controller
 Kernel driver in use: i915

Do you think this is possible?

I have intel and nvidia and my NVIDIA X-SERVER SETTINGS shows the settings.
Newest drivers doesn't always work for some people when it comes to linux systems since its mostly known from 3rd parties.
If you remember your previous drivers from ubuntu 14.04, you could work around with it.
So far i can't find any physical error with your system which is why i don't know how to help any more.

Thank you for your attempt to help.

Well, the fact that I do not have nvidia board (in addition to the intel board) must be the common denominator. I don't have two video cards, just an Intel® Haswell graphics card. I can't see where I can completely eliminate the intel drivers and use the nvidia drivers with my intel card.

My original problem remains unsolved: No HDMI output after upgrade to 16.04!