Updates Fail: Error Code 80070570 and 80073712

That looks right as well.
Perhaps the file is corrupted, or the permissions are wrong??

Please run the following command, and post the results

ICACLS C:\Windows\winsxs\amd64_microsoft-windows-servicingstack_31bf3856ad364e35_6.1.7601.17592_none_672ce6c3de2cb17f\CbsCore.dll

(all one line!)

Also, please zip the file up and upload it to your reply.

The permissions are definitely not right - but on the other hand, the aren't wrong in a very bad way.
Something has given Everyone permisssions to everything - and that's a definite no-no, since it removes the protections that the system has against malware and PEBKAC
The file there is OK - its 256Hash at least is the same as mine.

I wonder if there's a fake file present?

Open an Elevated Command Prompt, and run the following command...

DIR C:\WIndows\cbscore.dll /S

it'll take a minute or two to search - post the results.

Sorry for the delay!

let's start again from scratch...

Please follow the Windows Update Posting Instructions and post the requested data

If the file is too large (8MB compressed), remove the older CBSPersist cab files until the final file is below the limit - you can always post them separately after zipping them. (the forum doesn't allow the upload of bare CAB files, for a number of reasons)

Please also post the C:\Windows\windowsudpate.log file

CBS and Windows Update Logs attached.

Cheers :)

You don't appear to have run either SFC or CheckSUR again - and there is considerable evidence of problems in CheckSUR that SFC may or may not be able to deal with.

Please run both tools, and post the new logs.

Fresh logs attached.

CheckSUR ran and completed 1 update.

SFC stopped at the usual 18% with the same error message.

Thanks for looking at this.

Cheers :)

Here's the summary from the latest CheckSUR log...

Code:

Summary:
Seconds executed: 2309
 Found 135 errors
  CSI Payload File Missing Total count: 135

A quick look tells me that many of the files are from IE11 (11.2.9600.17501)

The CBS.log (SFC log) crashes at this point...

Code:

2015-05-04 23:40:46, Info                  CSI    00000080 [SR] Beginning Verify and Repair transaction
2015-05-04 23:40:47, Error                 CSI    00000081 (F) STATUS_FILE_CORRUPT_ERROR #1814750# from Windows::Rtl::SystemImplementation::DirectFileSystemProvider::SysCreateFile(flags = (AllowFileNotFound|AllowSharingViolation|AllowAccessDenied), handle = {provider=NULL, handle=0}, da = (SYNCHRONIZE|FILE_READ_ATTRIBUTES|FILE_READ_DATA), oa = @0xa2ccf0->OBJECT_ATTRIBUTES {s:48; rd:NULL; on:[129]"\SystemRoot\WinSxS\amd64_microsoft-windows-a..de-compat-telemetry_31bf3856ad364e35_6.1.7601.18653_none_e5a5eb8210168b23\aeinv.dll"; a:(OBJ_CASE_INSENSITIVE)}, iosb = @0xa2cda0, as = (null), fa = 0, sa = (FILE_SHARE_READ|FILE_SHARE_WRITE|FILE_SHARE_DELETE), cd = FILE_OPEN, co = (FILE_NON_DIRECTORY_FILE|FILE_SYNCHRONOUS_IO_NONALERT), eab = NULL, eal = 0, disp = Invalid)
[gle=0xd0000102]
2015-05-04 23:40:47, Error                 CSI    00000082@2015/5/4:11:40:47.639 (F) d:\win7sp1_gdr\base\wcp\sil\merged\ntu\ntsystem.cpp(2057): Error STATUS_FILE_CORRUPT_ERROR originated in function Windows::Rtl::SystemImplementation::DirectFileSystemProvider::SysCreateFile expression: (null)
[gle=0x80004005]
2015-05-04 23:40:47, Info                  CBS    Failed to retrieve CBS log environment variable size for offline WER report. [HRESULT = 0x800700cb - ERROR_ENVVAR_NOT_FOUND]
2015-05-04 23:40:47, Info                  CBS    Failed to add CBS log files to Windows Error Report. [HRESULT = 0x800700cb - ERROR_ENVVAR_NOT_FOUND]
2015-05-04 23:40:47, Error                 CSI    00000083 (F) STATUS_FILE_CORRUPT_ERROR #1814749# from Windows::Rtl::SystemImplementation::CDirectory::OpenExistingFile(...)[gle=0xd0000102]
2015-05-04 23:40:47, Error                 CSI    00000084 (F) STATUS_FILE_CORRUPT_ERROR #1814748# from Windows::Rtl::SystemImplementation::CDirectory_IRtlDirectoryTearoff::OpenExistingFile(flags = (MissingFileIsOk|SharingViolationIsOk|AccessDeniedIsOk), da = (SYNCHRONIZE|FILE_READ_DATA), oa = @0xa2d398->SIL_OBJECT_ATTRIBUTES {s:40; on:"aeinv.dll"; a:(OBJ_CASE_INSENSITIVE)}, sa = (FILE_SHARE_READ|FILE_SHARE_WRITE|FILE_SHARE_DELETE), oo = (FILE_SYNCHRONOUS_IO_NONALERT|FILE_NON_DIRECTORY_FILE), file = NULL, disp = Invalid)
[gle=0xd0000102]

It looks like you may have some filesystem problems...

Please run a full CHKDSK and SFC scan....
Click on Start > All Programs > Accessories
Right-click on the Command Prompt entry
Select Run as Administrator and accept the UAC prompt - the Elevated Command Prompt window should pop up.
At the Command prompt, type
CHKDSK C: /R
and hit the Enter key.
You will be told that the drive is locked, and the CHKDSK will run at the next boot - hit the Y key, and then reboot.
The CHKDSK will take a few hours depending on the size of the drive, so be patient!
After the CHKDSK has run, Windows should boot normally (possibly after a second auto-reboot) - then run the SFC.

SFC -System File Checker - Instructions
Click on Start > All Programs > Accessories
Right-click on the Command Prompt entry
Select Run as Administrator and accept the UAC prompt - the Elevated Command Prompt window should pop up.
At the Command prompt, type
SFC /SCANNOW
and hit the Enter key
Wait for the scan to finish - make a note of any error messages - and then reboot.

Upload the CBS.log file (compressed, please!) to your reply.