I have a PC with 2 HDD with 2 Vista OS at each other. One system is old and it has Python 3.7 installed and working successfully. The second system is new-installed and it has a problems with running web-based installers and executable-installer of the latest Python`s version from there: https://www.python.org/downloads/windows/ 

So I can run an install from any MSI-package for every version, but 3.5-3.7 versions don`t have it. When I`m trying to install wb-inst or exe-inst nothing happens: no error window, no system lags etc. 

I suppose that this problem connected with Microsoft libraries or extensions. I installed all Visual Studio C++ packages, but it didn`t help. 

Could you tell me which components I forgot to intall.

When you run the installer, it should create log files in your %TEMP% directory. Could you find and attach those here please?

There's a chance it is detecting that your system is unsupported. If you are still using Windows Vista, ensure you have installed all available updates and service packs, and then try installing Python 3.6 (the latest version, 3.7, does not support Windows Vista any more).