Hello there @Iceman187!
Checking around the community, if you are looping between restart and install, there’s a chance that Windows’ UAC is stopping your process without notifying you. I would either disable User Account Control temporary, or enforce admin rights with the installer (right click on the Launcher and pick “Run as Administrator”).
If the issue persists, you can bypass the launcher and install Epic Online Services directly. Simply go to C:\Program Files (x86)\Epic Games\Launcher\Portal\Extras\EOS and look for file EpicOnlineServices.msi to install the package.
Now, if the process has left any stale data, that continues to point to the same result, you can clear that up, by going to your Local App data folder, and eliminating folder EpicGamesLauncher\Saved. After that, try to install again.
