My guess you are using either Windows 95 or Windows 98. They dont have the option to Auto shutdown. Only Win XP has that option and Windows 2000. So you will be stuck hitting the power switch until you upgrade.
i beleive that 'Soft Power Off' which is what turns your desktop machine off automatically was introuced in Windows 98 (and was partially supported by WIndows 95 OSR2).
The machine must have the capability itself - it is not just software.
I had a quick look on Google but I'm not sure if it supports this function.
Your PC was probably made in around 1685. I would suggest buying a new one, as older versions are more prone to power shortages because of mischievous Magnemites causing trouble at the Power Plant near Cerulean City.