Windows Update Error 0x800b0100

PLEASE don't run the CLeanup tool - or any other tool - during this period. It can cause problems.

Having said that -SFC is now clear.

I haven't yet seen the report from the CheckSUR/SURT tool?
Please post that.

Strange - it's not an error I would expect from the tool.
All I can think is that the certificate store is corrupt in some odd way.
Try this...

This could be due to corruption in the SoftwareDistribution folder - the problem with that*the conventional cure *can lead to problems later on, if not handled properly, and you will lose your Update history (but the updates will still be installed, and viewable in the Installed Updates listing).
*
Open an Elevated Command Prompt
Run the following commands
*
NET STOP WUAUSERV
REN C:\WINDOWS\SoftwareDistribution SDOLD
NET START WUAUSERV
*
reboot
then wait 10 minutes, and open Windows Updates, and run a Check for Updates. (it could take a loooong while!)
*
DO NOT install any updates yet - but try the CheckSUR/SURT tool again and see if it behaves now

Let's have a look at a few other logs...

Please post the C:\Windows\windowsupdate.log file
Also...
Open Event Viewer
click on the Windows logs entry in the left pane to expand it.
Now click on the Application entry - wait while it loads.
Click on 'File' in the menu bar and select Save...
Save the file as Appevt.evtx
Repeat for the System log
then zip both, and upload them.

You appear to be having problems with multiple disks/partitions.
Drive D: has 8 bad blocks
Drive F: has had to be repaired multiple times recently
Drive C; has also been repaired a few times.

It's likely that this has introduced errors into the system in the registry, if not elsewhere, and I suspect that you need to think seriously about replacing at least drive D before attempting a repair install, to fix the system problems.

Great! - good luck.