Installing MS Visual C++ Redistributable fails due to manifest error

[MS-User]

Hi,
When trying to install the latest MS Visual C++ (downloaded the latest vc_redist.x64.exe), the installation fails with the following error message:

[0994:08AC][2018-06-24T15:19:36]i001: Burn v3.7.3813.0, Windows v6.1 (Build 7601: Service Pack 1),
path: D:\vc_redist.x64.exe, cmdline: ''
[0994:08AC][2018-06-24T15:19:36]e000: Error 0x80040154: Failed to load manifest as XML document.
[0994:08AC][2018-06-24T15:19:36]e000: Error 0x80040154: Failed to load manifest.
[0994:08AC][2018-06-24T15:19:36]e000: Error 0x80040154: Failed to initialize core.

When trying to uninstall the most recent version I have on the computer (2013), I get basically the same error message:

[0A7C:119C][2018-06-24T15:49:31]i001: Burn v3.7.2002.0, Windows v6.1 (Build 7601: Service Pack 1), path: C:\ProgramData\Package Cache{ce085a78-074e-4823-8dc1-8a721b94b76d}\vcredist_x86.exe, cmdline: '/uninstall'
[0A7C:119C][2018-06-24T15:49:31]e000: Error 0x80040154: Failed to load manifest as XML document.
[0A7C:119C][2018-06-24T15:49:31]e000: Error 0x80040154: Failed to load manifest.
[0A7C:119C][2018-06-24T15:49:31]e000: Error 0x80040154: Failed to initialize core.

I can (could, didn't do it) uninstall the next older versions (2008 and 2005).
My OS is: Windows 7 Home Premium 64 bit SP1

What I did so far (trying to install C++ after avery step, without success):
- sfc /scannow --> everything fine
- chkdsk --> everything fine
- manually re-registered both the 32-bit and 64-bit MSXML6 Dlls
- re-installed MSXML6 from here: http://www.microsoft.com/downloads/en/details.aspx?FamilyID=993c0bcf-3bcf-4009-be21-27e85e1857b1&displaylang=en

After this step, Windows found Update KB3118401 which I installed but which didn't help either.

- Updated MSXML4, then Windows found Update KB2758694 which I installed. Didn't help.

I guess the solution is to be found somewhere in MSXML. Maybe I am missing another optional update (all other updates have been done). But which one could it be?

Any help is appreciated - what other information do you need from me to be able to help?

Thank you.