I have updated three of my five home computers to 8.1 now, my main (this) computer (a homebuilt screamer), my own older (c. 2010) HP laptop, and my wife's newer and hotter HP laptop. On my older laptop, because I seldom use it for "production" work, I first updated it to Windows 8.1 Demo, which also exhibited a similar symptom (hanging at 42%) but they permitted you download the .iso for the demo version, which installed fine. I was able to install 8.1 from the store on that computer without a hitch, but it hosed all my apps (as Microsoft had duly warned me would happen).
But on my wife's laptop, where Windows 8 had come preinstalled by HP, and on mine on which Windows 8 was installed over Windows 7 without a hiccup from a store-bought disk on the first day of public release, both exhibited this same symptom. Both systems were fully up-to-dat in the O/S, all drivers, and BIOS, completely clean of malware of any kind, and I had previously REMOVED (not deactivated) my third-party anti-malware and firewall apps, and for the installation deactivated even Windows Defender. I am on a very fast and reliable Internet connection (FiOS Quantum)
At this time Microsoft was not offering an .iso file for download. I am pleased to see that they have relented on this point. They had forced their end users to rely exclusively on the Store for this update.
My solution was to deal with this "the old fashioned way." I called Microsoft Technical Support on the phone. After literally hours at two different times on each machine, where their tech was using remote access to tromp around all over my computers, and with both cases involving an escalation to a higher-level tech who called me back the next day, FINALLY it got installed, on my home-built through the store and on my wife's HP laptop via download of the .iso file and installing from that.
The good news is that all has been well ever since, with the only cleanup work being the need to reinstall my HP AIO full-featured printer drivers (the basic printer driver still worked after the update).
Good product. BAD delivery. Surprisingly prompt technical support under what must've been trying circumstances.