I had this issue too. This experience hosed my current running copy of Windows 10. Fortunately, it wasn't long ago that I took a snapshot so I didn't lose much. I can't be certain that your cause is mine, but after playing with my latest snapshot and having a similar experience of failing Parallels installs several times with that annoying network error, I figured out that it was IOBIT Uninstaller automatically "cleaning" (uninstalling) the Parallels Installer tool before it was done with the installation.
So I did a snapshot restore again, then as soon as Windows booted, I was able to get into IOBITS Uninstaller settings and turned off Auto clean/ auto uninstall options before Parallels Tools Installer got to the section where it does some cleanup operations. My Windows 10 guest VM is fine now.
The specific settings in question are:
Automatically remove residual files.
Delete leftover files to Recycle Bin.
Automatically delete leftovers of program uninstalled by other uninstaller.
That being said, I'm not sure how one would fix your issue if you don't have a snapshot handy, but maybe it would shine a light on exactly where your issue is for someone who knows how to go in and restore/fix damaged system configurations.