That worked on my laptop, even with wifi turned off. So I traced it with Process Monitor. I see it using the Admin$ share, presumably because it is designed to work on another pc. The help output says, "PsExec executes a program on a remote system". So it would appear that whatever network configuration you have, does not implement an Admin$ share.
Why do you need to run the task scheduler as the system account?
Create a scheduled task, that runs as the system account, and use the command line schtasks.exe or a Powershell script to do whatever you need to do.