Using the online installer, I got numerous "error during installation process" dialogs.
"Start Menu\Programs\Accessories\C:\Users\GP" - that does not look correct.
Just found the installation log file. All the errors were caused by failure to create a shortcut in the start menu. The installer gave me a choice of whereabouts in the start menu to create the shortcuts. Of these choices, the only one that looked vaguely reasonable was "accessories" so that's what I chose.
Operation 'CreateShortcut' with arguments: 'C:\GP\Qt\5.3\msvc2012_opengl/bin/designer.exe; C:\Users\GP user\AppData\Roaming\Microsoft\Windows\Start Menu\Programs\Accessories\C:\Users\GP user\AppData\Roaming\Microsoft\Windows\Start Menu\Programs\Qt/5.3/MSVC 2012 OpenGL (32-bit)/Designer.lnk' failed:
created warning message box installationErrorWithRetry: 'Installer Error', Error during installation process (qt.53.win32_msvc2012_opengl):