I have the same problem. Version 7.1.0.3 x64 did install without errors. When trying to start it hung on a ‘final’ splash screen, no errors. I left it for about 8 hours, no changes. After killing the task i then uninstalled it and reinstalled it, same persisting problem. I then tried the 7.0.3 x64 version, same probem, also hung on the final splash screen.
I then tried the 7.0.3 x32 version of Libreoffice. It took a little time, but Writer did start after a about a minute. I noticed some things were setup by Writer after starting it the first time and prior to getting the main Witer window. The second time i started Writer it started quite fast. So there is some sort of post install preparation being done at first time start.
I then started the 7.1.0.3 x64 installer again. It removed parts of the previous 7.0.3 x32 installation and then installed without error. I then started Writer, and it started immediately, no errors, no problems. My best educated guess is that the x64 versions of LibreOffice installer has post installation and pre first time run setup issues which causes LibreOffice to hang on the splash screen.
Other users seem to confirm that the problems seems to be related with the user profile that is being setup by LibreOffice x64. Perhaps my experience can point you to a solution for the x64 installers.
My Windows 10 version is the latest 20H2 version, Build 19042.804, with minimal application setups and all updates applied. Some of the hardware drivers, like for the videocard, are outdated (2016) as this is a HP Pavillion DV7 laptop which has switchable graphics between Intel HD 3000 and AMD Catalyst 15.7. The OpenGL Extension viewer 5.02 reports version 3.1 of OpenGL, the latest 6.18 version simply crashes when querying the Intel HD Graphics 3000 videocard.
So for now, install the x32 version, then upgrade to the x64 version.