Error while trying to install SQL Server Management Studio 2016 (version 17.3)

OS: windows 8.1 enterprise, 64 bit (download link)

I've successfully installed SQL Server itself, except the SDK which had a similar error. While installing the package of SSMS, I get an error prompt and the action fails (same error appears in below log file). The same error occurs when I try to install the 2014 version.

I tried to repair and also reinstall some prerequisites:

• Microsoft Visual Studio 2015 Shell (Isolated)
• Microsoft Visual C++ Redistributable (x64) - 14.0.24215
• Microsoft Visual C++ Redistributable (x86) - 14.0.24215

From the log file:

[153C:05C8][2017-11-28T09:42:11]e000: BootstrapperEngineDataModel.OnError: Burn engine encountered error. PackageId: sql_ssms_extensions_x86, ErrorType: WindowsInstaller, ErrorCode: 1935, Data: 1935,{A6E5F44D-C641-4A67-A876-5E0F8C4AC1AD},0x80070570,IAssemblyCacheItem,Commit,Microsoft.SqlServer.Management.IntegrationServicesEnum,fileVersion="14.0.1000.169",version="14.0.0.000000",culture="neutral",publicKeyToken="89845DCD8080CC91",processorArchitecture="MSIL", ErrorMessage: An error occurred during the installation of assembly 'Microsoft.SqlServer.Management.IntegrationServicesEnum,fileVersion="14.0.1000.169",version="14.0.0.000000",culture="neutral",publicKeyToken="89845DCD8080CC91",processorArchitecture="MSIL"'. Please refer to Help and Support for more information. , UIHint: 0 [153C:05C8][2017-11-28T09:42:11]i000: MainViewModel.AddFailedCondition: Error: SQL Server 2017 Management Studio Extensions: An error occurred during the installation of assembly 'Microsoft.SqlServer.Management.IntegrationServicesEnum,fileVersion="14.0.1000.169",version="14.0.0.000000",culture="neutral",publicKeyToken="89845DCD8080CC91",processorArchitecture="MSIL"'. Please refer to Help and Support for more information. [153C:05C8][2017-11-28T09:42:11]e000: MainViewModel.OnPackageError: setup failed for packageId: sql_ssms_extensions_x86, package: SQL Server 2017 Management Studio Extensions, errorCode: 1935, errorMessage: An error occurred during the installation of assembly 'Microsoft.SqlServer.Management.IntegrationServicesEnum,fileVersion="14.0.1000.169",version="14.0.0.000000",culture="neutral",publicKeyToken="89845DCD8080CC91",processorArchitecture="MSIL"'. Please refer to Help and Support for more information.

Any ideas?

EDIT: I tried to brute-force solve it by:

1. Uninstalling everything which has to do with SQL (of all version) on my machine
2. Uninstalling everything which has to do with Visual studio (of all version) on my machine
3. Deleting all folders which have to do with Visual studio or SQL (of all version) from my machine
4. Editing the registry so as to remove all traces of Visual studio or SQL from my machine
5. Reinstalling SQL server 2016 (was successful)
6. Reinstalling SSMS 17.3 (failed with the exact same error!)

The error being:

An error occurred during the installation of assembly 'Microsoft.SqlServer.Management.IntegrationServicesEnum,fileVersion="14.0.1000.169"

If no answer, my next action is to format the entire machine and reinstall everything.