DLL load failed: Unable to use GDAL on windows

When I am trying to load GDAL I get:

C:\Windows\System32>python
Python 3.5.2 (v3.5.2:4def2a2901a5, Jun 25 2016, 22:18:55) [MSC v.1900 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> from osgeo import gdal;
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "C:\Python35\lib\site-packages\osgeo\__init__.py", line 21, in <module>
    _gdal = swig_import_helper()
  File "C:\Python35\lib\site-packages\osgeo\__init__.py", line 17, in swig_import_helper
    _mod = imp.load_module('_gdal', fp, pathname, description)
  File "C:\Python35\lib\imp.py", line 242, in load_module
    return load_dynamic(name, filename, file)
  File "C:\Python35\lib\imp.py", line 342, in load_dynamic
    return _load(spec)
ImportError: DLL load failed: The specified module could not be found

How to know, which DLL it wants? If it reported it's name, I would check the path.

For now I have installed this

http://download.gisinternals.com/sdk/downloads/release-1500-x64-gdal-2-1-3-mapserver-7-0-4/gdal-201-1500-x64-core.msi

and this

http://download.gisinternals.com/sdk/downloads/release-1500-x64-gdal-2-1-3-mapserver-7-0-4/GDAL-2.1.3.win-amd64-py3.4.msi

I have Python in C:\Python35 and set it explicitly for while latter install.

Paths are set:

>echo %PATH%
C:\Python35;C:\Program Files\GDAL;C:\Python35\Scripts;

Variables are set

>echo %GDAL_DATA%
C:\Program Files\GDAL\gdal-data

>echo %GDAL_DRIVER_PATH%
C:\Program Files\GDAL\gdalplugins

What else voodoo to try?