How to shut down a remote computer
 

This can be done only if the computer is logged on.
There's a small utility called "SHUTCMD.EXE" included in the Windows NT Resource Kit that can be used to shutdown or restart a local or remote computer.

For example, you can shutdown the local computer by running:
SHUTCMD /L

to shutdown a computer on a network ("SYTEM1" being the name of the system to be shutdown):
SHUTCMD \\SERVER1 /Y

to shutdown a remote computer connected to the Internet ("101.36.22.14" being the IP address of the computer you want to shutdown):
SHUTCMD \\101.36.22.14 /Y