Per "Python 3.5.0 (32-bit)_20150914055131.log", the installer detects the OS as NT 6.2.9200 (Windows 8/Server 2012), and installs Windows8-RT-KB2999226-x64.msu.

    [0A68:0EC8][2015-09-14T05:51:31]i001: 
      Burn v3.10.0.1823, 
      Windows v6.2 (Build 9200: Service Pack 0), 
      path: C:\Users\mg\Downloads\python-3.5.0.exe

    [0F48:03B4][2015-09-14T05:54:05]i301: 
      Applying execute package: crt_14.0_v6.2_x64, 
      action: Install, 
      path: C:\ProgramData\Package Cache\
            0F275C704EE13CA9E98834DB6DA50D4693FF2BAF\
            Windows8-RT-KB2999226-x64.msu, 
      arguments: '"C:\Windows\SysNative\wusa.exe" 
                  "C:\ProgramData\Package Cache\
                   0F275C704EE13CA9E98834DB6DA50D4693FF2BAF\
                   Windows8-RT-KB2999226-x64.msu" 
                  /quiet /norestart'

which seems to succeed: 

    [0A68:0EC8][2015-09-14T05:54:24]i319: 
      Applied execute package: crt_14.0_v6.2_x64, 
      result: 0x0, 
      restart: Required

Yet trying to run py.exe to compile the standard library fails with STATUS_DLL_NOT_FOUND (0xC0000135):

    [0F48:03B4][2015-09-14T05:55:11]i301: 
      Applying execute package: compileall_AllUsers, 
      action: Install, 
      path: C:\ProgramData\Package Cache\
            1D1205B0F2D3B4B31CC368C86271206AEF327163\py.exe, 
      arguments: '"C:\ProgramData\Package Cache\
                   1D1205B0F2D3B4B31CC368C86271206AEF327163\py.exe" 
                  -3.5-32 -E -s -Wi "C:\Python35\Lib\compileall.py" 
                  -f -x "bad_coding|badsyntax|site-packages|py2_|
                         lib2to3\\tests|venv\\scripts" 
                  "C:\Python35\Lib"'

    [0F48:03B4][2015-09-14T05:57:24]e000: 
      Error 0xc0000135: Process returned error: 0xc0000135

Your screenshot shows that api-ms-win-crt-runtime-l1-1-0.dll is missing. Does this DLL exist in "%SystemRoot%\SysWOW64"?