Is there a way to remotely shut down a Windows machine on my home network that doesn't support RDP?

Such "highly trusted" code already exists.

• The shutdown tool can do remote shutdowns over RPC, as long as File Sharing is enabled:

  shutdown -m \\plexbox -s -t 0 -f
  

  Its Linux Samba equivalent:

  net rpc -S plexbox -f -t 0
  

  (Note that this needs SeRemoteShutdownPrivilege separate from the regular "local shutdown" privilege – even if you use it locally. This can be granted to non-admins via secpol.msc.)

• PowerShell Remoting can be used to run PowerShell commands.

• You can install a SSH server, such as Bitvise WinSSHd.

• psexec was the usual pre-Remoting tool for running programs remotely. (Although I can't get it working with Active Directory anymore...)

• Finally, as GeraldB also wrote, there are other graphical remote control tools besides RDP – such as VNC, TeamViewer, radmin, etc.

VNC (TightVNC or many other flavors) is a freeware graphical remote control solution like Remote Desktop you wanted to use. It supports Windows 8.x. VNC though a SSH tunnel is recommended for usage across the Internet.

Alternatively if you enjoy the command line, try running an SSH server on your media server. You can then run an ssh client (like PuTTY) which would allow the automation of file transfers and access to the command line with high security. Inside of an ssh session or even directly from another Windows machine, you can use the shutdown command-line. This allows you to shut down or restart a local or remote computer.

For a low-tech solution, try holding the power button down quickly for a second or less (not the 5 seconds for a hard power off). Windows should shutdown gracefully or go into standby, depending on configuration.

As Peterh mentioned, you can also use telnet a command-line interface built-in to windows. See control panel, add-remove programs. While telnet is insecure for a home network it is a possibility. SSH is the recommended secure encrypted alternative that only takes a little longer to setup.

Find an old computer with a CD-ROM drive. Install linux. Name it HOMECOMPUTERSHUTDOWNROBOT. Find a plastic stick, about 2 inches long. Superglue it to the CD-ROM door so that it sticks straight out from the computer. Position the old computer so that the stick points at the power button for the computer you want to shut down. Use old books as necessary to prop the computer up to the needed height to do so.

When you want to turn off the computer, SSH into HOMECOMPUTERSHUTDOWNROBOT. In the terminal, use the eject command to eject the CD drive. The plastic stick will push the power button of the computer not supporting RDP and turn it off.