Which method is NOT suitable for gathering information from a Windows machine without an interactive shell?

The method that is not suitable for gathering information from a Windows machine without an interactive shell is connecting to the system using Remote Desktop Protocol (RDP). RDP requires an interactive session where a user must log in and engage with the desktop environment, which does not align with the requirement of gathering information without an interactive shell. This method is inherently designed for remote graphical access where the user can interact with the operating system and applications directly.

In contrast, the other options allow for information gathering through command line or scripting interfaces, which do not require an interactive user session. The wmic command-line tool provides a way to query system information through scripts, the ping command can be executed to check for network connectivity without needing a user interface, and the Get-NetTCPConnection cmdlet in PowerShell retrieves information about active TCP connections, also possible without an interactive shell.