ubuntu 14.04 black screen when installing

I had this problem and solved using the nomodeset mentioned by @Xubu-Tur along with the nolapic. This last one was necessary otherwise it woudn't work, but I am assuming you can get to the installation window (it is not clear in your question), like shown below:

EDIT:

I see. I think the options beneath allow you to edit the boot parameters. If that is the case, then you can set the boot parameters adding "nomodeset" and "nolapic" to the same place of the "quiet" and "splash". In the end it should be something like (...) quiet splash nomodeset nolapic (...). In the link you provided in the question there is an example (the guy removed the quiet splash, but I don't think that is necessary).

Add this to the kernel booting options (as specified by marcelocra user in one of the comments):

quiet splash acpi=off nolapic nomodeset

Important note

Because of nolapic you will have only a single cpu and core visible, hence you should disable this for a later usage.

I had same problem on Ubuntu 14, 15 and 16 on CD or USB but confusingly was able to install Win10 from CD.

What it turned out was the cdrom drive was connected to SATA port with AHCI - Ubuntu has a problem with that.

With nomodeset and splash off (so you can see where it fails) I was able to identify it to ATA problem.

Disconnecting the CD I was able to install Ubuntu 16.04 without issue (I might have had nomodeset).

Then reconnected it to non-AHCI SATA port after installation complete.