Windows 8 do shut down - HEWLETT-PACKARD HP ProBook 6550b Notebook

To turn Off your Windows 8 PC, you can click the Power button on your screen and then click "Shut Down". If there is no Power button on your screen, you can follow the instructions below:
1. Swipe in from the right edge of the screen, and then tap "Settings".
(If you're using a mouse, point to the lower-right corner of the screen, move the mouse pointer up, and then click "Settings".)
2. Now, click or tap Power and then, click or tap "Shut Down".
The following link can be useful:
http://windows.microsoft.com/en-IN/windows-8/how-shut-down-turn-off-pc

Hope this will help you.

GuruAid.com

1. In Windows 8.1, from the Start screen, click the Power button and select Shut down.
If you can't see Start screen, point the mouse to the bottom-right corner of the screen, click Settings, then click Power, then click Shut down.

2. From the Start button, select Shut down or sign out and then Shut down.

1. In Windows 8.1, from the Start screen, click the Power button and select Shut down.
If you can't see Start screen, point the mouse to the bottom-right corner of the screen, click Settings, then click Power, then click Shut down.

2. From the Start button, select Shut down or sign out and then Shut down.

go to start click your account name choose shut down

Try holding the shift key down while selecting restart, then select "Turn off your PC."

Then power it back on normally. Startup will likely be a little longer than normal.

(The default "Shutdown" option in Windows 8 actually just hibernates your laptop.)

It might be to do with Windows 8, but what would be overheating is your processor or RAM. If it is the battery, Windows 8 might be too much drain, or it's simply coincidence and your battery is had it.

This WEB site explains how.
http://www.pcworld.com/article/2012202/how-to-shut-down-windows-8.html

For a details check out this WEB site.
http://www.pcworld.com/article/2012202/how-to-shut-down-windows-8.html

Hold the power button down until it shuts down.

In windows 8, Set to High Performance, set Sleep and Hibernate to Never, set What to do when Lid is closed, adjust Advanced Power Options to your preference. Always Shut Down the Laptop and unplug when not in use to prevent damage due to power surges. Use this procedure: http://techmell.com/windows-tips/change-windows-8-power-options-launch-setting-details/