http://www.zdnet.com/windows-8-1-consumers-its-time-to-move-to-update-1-7000030378/ and http://www.cnet.com/news/windows-8-1-patches-wont-install-without-april-update/
The vast majority of folks have had no problem with this update (well, according to Microsoft)
All cases I've recently opened have had the same resolution:
Reinstall
Find repair media from someplace on the web
rebuild
The servicing stack is so corrupted nothing is working.
I am seeing no other solution, no magic fix. I'm sorry for no better resolution than this.