Please attach "Python 3.5.0 (32-bit)_*_core_JustForMe.log", if it exists.

According to the log, initially the installer can't create a restore point because, I assume, you have the volume shadow copy (VSS) service disabled, i.e. the error code is ERROR_SERVICE_DISABLED (0x80070422). That shouldn't derail the installation, but it's unusual to disable this service since restore points are critically important in case something goes wrong while modifying the system.

Next, installing core.msi fails with the error code ERROR_INSTALL_ALREADY_RUNNING (0x80070652). This means you had an existing installation in progress. Check for running instances of msiexec.exe. If the existing installation process is hung, try installing Python 3.5 again after rebooting.