SSDT installation issue (Failed to execute EXE package.)

The answer from Nick is very helpful, but I still failed at SSDT-Setup-ENU.exe /repair with the same error Error 0x800703e9: Failed to execute EXE package..

Then I tried it with a very straightforward way: (Disable UserAccountControl first)

1. copy SSDT-Setup-ENU.exe to c:\temp and execute SSDT-Setup-ENU.exe /layout to download a local copy of the bundle.
2. open C:\temp\redist and double click NDP461-KB3102438-Web.exe
3. open C:\temp\payload and double click vsta_setup.exe
4. repeat to install others...

This is the most likely link I came to when I got the same message in my log:

Applying execute package: Microsoft.DataTools.AnalysisServices, action: Install, path: C:\ProgramData\Package Cache\9864EE5369359DB622D0234B6C6B7640B949140C\VSIXBootstrapper.exe, arguments: '"C:\ProgramData\Package Cache\9864EE5369359DB622D0234B6C6B7640B949140C\VSIXBootstrapper.exe" /q /admin /instanceIds:"fc3f0e2c" /logFile:"C:\Users\a_nzchuk\AppData\Local\Temp\SsdtSetup\SSDT-Setup-ENU_20171205113839_002_Microsoft.DataTools.AnalysisServices.log" "payload\Microsoft.DataTools.AnalysisServices.vsix"' 
MainViewModel.OnPackageActionProgress: Percent completed: 50, Overall progress: 17 
MainViewModel.OnPackageActionProgress: Percent completed: 50, Overall progress: 17 
........... 
...
Error 0x800707d3: Process returned error: 0x7d3
Error 0x800707d3: Failed to execute EXE package.
Error 0x800707d3: Failed to configure per-machine EXE package.
MainViewModel.OnPackageAction: Install Completed for package SQL Server Analysis Services (id: Microsoft.DataTools.AnalysisServices)
Applied execute package: Microsoft.DataTools.AnalysisServices, result: 0x800707d3, restart: None

So I'll document my findings here.

In my start menu I had Visual Studio 2017 (SSDT). It ran OK but didn't have any BI projects available

This is what I did from an Administrator elevated command prompt:

1. Copied SSDT-Setup-ENU.exe into C:\temp (rather than a user specific download folder which the admin user may not have access to)
2. Ran SSDT-Setup-ENU.exe /layout to pre-download support and redist files (this was after a required restart)
3. Ran SSDT-Setup-ENU.exe /repair to try and repair the install. It gave me a button Repair that I clicked.
4. Ran SSDT-Setup-ENU.exe /repair again. Selected Modify. Noted that only SQL Server Database was ticked, but none of the others (SSAS, SSIS, SSRS)
5. Ticked SQL Server Analysis Services and pressed Modify. It proceeded to do it. Got stuck at 50% for a few minutes but eventually worked
6. Repeated for SQL Server Reporting Services and SQL Server Integration Services

After this, when I reran VS2017, it had the BI projects and allowed me to create a 1400 SSAS solution