Error: 0x80073712 when installing KB 2919355

I agree and understand you frustration and I dislike Microsoft for a list of issues that have personally affected me, however you've got to do what you've gotta do to fix the corruption within the component store and the only way to do so at this point is by finding a friend or family that can lend you their disk if they have one or download a copy from a software forum.  Check out the one I mentioned, and once you're registered (takes 30 seconds or less), click on apps, then go to the bottom of the page and in the search box, type "windows 8.1 [followed by your type and architecture] msdn"  Once you've found one where the hashes match, and have it download, do a virus scan of it as an extra precaution.  By the nights end, you can have your problem fixed.

Have you tried running windows update alongside the 8.1 installer, as mentioned in the following tutorial?  If not, give it a try as it should work.

***KB2919355 Fix that WILL allow the install of KB2919355***

As many discoveries have been made, I discovered this accidentally. and quite by coincidence... 

In order for users, who've been plagued by errors and file corruption, to get a successful completion of KB2919355, all that's needed is to run the 8.1 upgrade installer, and when the 8.1 installer goes to the wait screen after entering the generic product key, start Windows Update for the install of KB2919355

EDIT: It appears, from the input of other users, one must FIRST install the 5 standalone updates included within the Windows Update KB2919355 package, you will then need to restart after the fifth and final standalone, then use Windows Update to install KB2919355 (do not use the standalone installer for KB2919355... use Windows Update).

Steps

1. Run the Windows 8.1 installer from within Windows, as if you're going to do an install repair "upgrade".
2. Enter the generic product key, and upon clicking next, the installer will say wait...
3. Give the installer about 5 minutes, then start Windows Update (it should show the KB2919355 update), and click install.
4. Windows Update will begin downloading the update... if you have a Windows Update cache problem that causes the speed and percentage to remain at zero, don't worry about it and get the update installed first, then you can clear the cache and remove the directories afterwards.
5. The install may fail, don't worry... simply hit install again, making sure the 8.1 installer screen is still on the "wait" screen, as whatever the installer is doing during the "wait" screen is what makes the KB2919355 install possible.
6. KB2919355 should install and Windows Update should request you to restart... simply do so without cancelling the 8.1 installer.  Windows will finalize the update during the shutdown and restart processes.
7. Upon rebooting into Windows, you will have a multitude of additional updates that will need to be installed (around 10, give or take a few), and you can verify the install of KB2919355 by going to "view installed updates"

A few users will need to comment back once they'e performed this in order to see if this automatically fixes the multitude of issues users are facing, and if it doesn't complete successfully, then I can back track what step I took over the past several days in order to figure out what caused this to work for me, but not others if problems occur.

We could all get the corruption repaired if the media was available for a repair/install, unfortunately the elephant in the room which created the corruption as a result of the update refuses to make it available and will not allow OEMs to make it available which leaves users with no alternative other than resorting to torrent or other similar sites. Pathetic and disgusting.