I downloaded the appropriate LibreOffice for my PC but the installation package won't open. How do I fix this? Please help.

You never installed any updates on your Windows 10, so I’d expect more and more problems in the future. Current OS Build for Version 1607 is 14393.2972 (as of 19th May 2019).

… and never receiving updates could indicate a disabled Windows Update Service but an active Windows Update Service is for some reason necessary for LO Installer.

… but in this case, the most possible thing is corrupt download. All update-related issues only could show up after successful launch of the installer.

A workaround: install the portable version.