Windows Update cannot check for updates, because it is not running

Alright, I've checked the posting instructions, and let's get that out of the way.

1. Tried to install SURT, I get the following error;

Installer encountered an error: 0x80070424
The specified service does not exist as an installed service

2. sfc /scannow
The verification was able to complete up to 58% at which it gave the error

Windows Resource Protection could not perform the requested operation

3. No Windows Update error codes, it just says 'Check for updates for your computer' with a big red X icon

4. Log collection
I tried to attach the CBS.zip but it's 10mb, and this forum has an 8mb limit.

Okay, so I am reserving Windows 10 for the various computers at home, and when I try to update this computer which I use as an HTPC, I know I need update KB3035583 to get the option to reserve Windows 10, but when I go to do so, Windows Update tells me it can't check for updates because it's not running. I tried manually turning it on via an elevated command prompt but that doesn't work. Any help would be appreciated! Thanks!

Update

So after some digging and some relevant posts here, I was able to fix the problem.
I know people hate when people don't post what exactly fixed their problem so....

I used Option 3 in the Windows Update Reset thread located here

BUT now I get a new error,

Windows could not search for new updates
Error Code 8024402F - Windows Update encountered an unknown error

after retrying, I get another error,

Windows could not search for new updates
Error Code 80080005 - Windows Update encountered an unknown error

After running Microsoft's Fix It for Windows Update, I get the error

Compressed (zipped) folders error
File not found or no read permission

With an OK button and I haven't found a way to run the Fix It as admin.

After Fix It completes, I get the following

Some security settings are missing or have been changed - Not Fixed
Windows Update error 0x80070003(2015-07-28-T-04_12_51P) - Not Fixed
Problems installing recent updates - Not Fixed
Problems installing recent updates - Not Fixed
Service registration is missing or corrupt - Fixed

with an 'Explore additional options' and some other buttons.

Any help would be greatly appreciated!