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I use a remote desktop program (usually Microsoft's Remote Desktop) to connect to a Windows machine everyday. The remote computer has a fixed IP address, and if the computer is on and responsive, I can reboot the computer remotely to install updates, etc., as well as turn it off.
Unfortunately, if the remote computer freezes (for example, if it gets a blue screen), as far as I know, I can't use a remote desktop solution to restart it. Similarly, if my computer is off, I can't use remote desktop to boot it.