Or try Raydun's refresh of Windows 8 using "custom install."
Some people say that re-installing Windows 8 from scratch cleared up the problem, but several people recommend that you not install any of the offered updates except KB2871389, which makes the Win81 upgrade visible in the Windows Store. My guess is that they took out an offending driver in the process -- but that's only a guess.
Still can't get Windows 8.1 installed? Do everybody a favor and drop by the main Microsoft Answers thread on the topic and post a polite gripe. Or even a mean gripe. Make sure you mention any weird hardware you might be using. And good luck.
By the way, if you encounter any other magical incantations that work -- chicken entrails most definitely included -- please post them as comments here.
This story, "Microsoft needs your help to nail the Windows 8.1 update 0xc1900101 Blue Screens," was originally published at InfoWorld.com. Get the first word on what the important tech news really means with the InfoWorld Tech Watch blog. For the latest developments in business technology news, follow InfoWorld.com on Twitter.