Cannot install Windows 8.1 Update KB 2919355

A working solution would be to do a repair installation. Insert the 8.1 dvd or iso file, start setup, select upgrade and it will repair windows and let you install updates afterwards.

Where's a good place to get Win 8.1 with updates iso?  I have 8.0 media, but not 8.1 with updates

Download 8.1 from Microsoft. Updates can be reverse integrated by
1 installing 8.1
2 updating it
3 using imagex.exe (part of WAIK) to create an updated install.wim from it
4 exchange install.wim on you USB setup medium

There's a lot of mighty big words in there, Mr. McKnife. And we are but simple folks here.  :)
I am vaguely familiar with WAIK.  Looking up ImageX, it sounds like it is imaging software like Acronis.  So, I'm going to create the 8.1 with update by downloading the ISO, and using Nero to burn to DVD.  And then use that disk to repair my 8.1 installation, hoping it will install the updates in the process.  Sound like a plan?

Sounds like, yes.
You wouldn't need to bother integrating updates, though. Repair and afterwards it will be able to use windows update again.

I'll let ya know!

i've seen this question come up a couple times here regarding that update
one was resolved by removing gpo restriction to usb devices because a driver for usb is updated and thus failed because of the gpo

if that doesn't apply to you, take a look at this article citing a KB update for systems that don't have 2919355 installed

Description of the security update for Internet Explorer 11 for systems that do not have security update 2929437 or 2919355 installed: May 1, 2014
https://support.microsoft.com/en-us/kb/2964444

Well, here is what I did.  Unfortunately, I called MSFT for help... shouldn't have wasted my time.  Summary:  this machine was a perfectly fine functioning PC with 8.1 Pro & Media Center.  Turned out, there was some corrupt files that was blocking the 8.1 Update.  So I downloaded 8.1 Pro ISO, burned DVD, and used that DVD to repair PC using the Refresh option.  When I tried to use the8.1 Pro DVD, it would not take my 8.1 Pro key?!?  This is the key that came out of the 8.1 Pro machine itself, activated, working for years, no problem except the Update.  So I thought, I will use the key from another 8.1 Pro machine to refresh this one, and then when its done, go in and put the old key back in.  Nope!  The machine is running fine, activated, updating... but, it will not take the old key (the one that was working fine for a year).  I called MSFT, they said that because I "broke the ladder of installations" the key wouldn't work anymore.  And wanted to charge me $199 to get a new one?!?!?  They said the only way to fix it is to take it back down to 8.0, go to the app store, and upgrade from there.  So I told them to take a hike!  Seriously thinking about selling my MSFT stock; truly poor.  Thanks to the folks that responded from EE.