I'm trying to delete everything on the desktop from a txt file containing computer names(40 pcs – separate domain). Maybe my syntax is off. I tried using invoke-command inside the foreach loop and wasn't successful either.
Your code is basically okay, assuming that you have appropriate rights on all of the computers you're connecting to (access to the c$ share, permission to remove files from users' desktops, etc. Basically, Administrator), with one exception. There is no C:\Users\Desktop folder. Instead, you want to remove the contents of the Desktop folder from each user profile found in C:\Users (assuming that user profile directories are their default values and haven't been redirected.) Try this:
I added the -WhatIf switch because this is a destructive command, and you might want to make sure you like what it's doing first. You might also want to add a -Recurse switch to the command, if there are folders on these desktops that you want to clear out.