I had the 0xc1900101 error as well, with 0x2000C. I did get this fixed, finally. Here's what worked for me on my HP Envy 23 inch all in one:
First, update the Intel 4000 Graphics driver direct from intel.com. I had to do this by first disabling the Intel Driver so the install would complete:
- Open Device Manager
- Expand Display Adapters
- Right Click on the Intel HD Graphics 4000, and choose Update Driver Software.
- Pick Browse My Computer for Driver Software
- Click "Let me pick from a list of device drivers on my computer"
- Scroll down and pick the "Microsoft Basic Display Adapter"
- Click next/OK until that's done.
- Reboot.
- Download an updated driver from Intel.com. My particular one was located here: https://downloadcenter.intel.com/Detail\_Desc.aspx?agr=Y&DwnldID=23405&lang=eng
- Install that, which will require another reboot.
After rebooting, do the following:
- Delete everything in C:$Windows.~BT
- Type Win+R, and run wsreset.exe
- Start the Store app
- Typed Win+I, picked App Updates, and then clicked Sync Licenses.
- Install Windows 8.1 from the Windows store.
Hopefully this works for other people.