Drive letters change when you boot to the Recovery environment - which is why I phrase the instructions the way I do :)
That deems to have fixed the file errors, at least, and nothing obvious has cropped up in the background CBS log, either.
Let's see if this gives us any more data...
Please download and save the CheckSUR tool from
System Update Readiness Tool fixes Windows Update errors in Windows 7, Windows Vista, Windows Server 2008 R2, and Windows Server 2008
(you'll need to look in the details for Windows 7, downloading from the Microsoft Download Center)
Run it - The tool can take anywhere from 5 mins to a couple of hours to run (or 'Install') depending on how much it has to do, and may exit silently - it may appear to freeze for most of that time, but be patient.
The result is logged in the C:\Windows\Logs\CBS\CheckSUR.log file - and an archive …\checksur.persist.log file
Then zip the CheckSUR.log and upload it to your reply.