Windows cannot install required files. The file may be corrupt or missing. (0x80070570)
Solution 1:
This is pretty much all speculation, but this is what seemed to be the case.
One of my RAM sticks is faulty (Windows Memory Diagnostics has since confirmed this). After removing it, I had no more trouble installing and using Windows. It appears this may have been the cause of the installation failure.
As for the original problem, my suspicions lie with a crash during a Windows update that rendered the disk unbootable.
Unfortunately I don't have any real evidence of what was happening, aside from the memory diagnostic result.