Q: ipod shuffle works in some computers but not others

When you say "charger," are you referring to a USB docking cable?  If so, it's just a cable.  If it works with a Mac and Windows 7 PC, but not a Windows 8 PC, the cause is probably a problem on the computer (that does not recognize the shuffle), not the cable. 

On the Windows 8 PC, try this procedure to restart the Apple Mobile Device Service

Restart the Apple Mobile Device Service (AMDS) on Windows - Apple Support

If that does not help, you may want to completely remove iTunes and related software components.  This Apple document lists all components of an iTunes installation, and the precise order to uninstall them

Remove and reinstall iTunes and related software components for Windows 7 and later - Apple Support

Then download and install the latest version of iTunes

http://www.apple.com/itunes/

There are four types of iPod shuffle.  Which "generation" is your shuffle?  This document shows the four types

Identify your iPod model - Apple Support

Also, if you bought this "generic" docking cable online, can you provide a link to the item you bought?

And one more bit of info that may be helpful.  When you connect the shuffle to the Windows 8 PC, watch the shuffle's light.  Does it blink (at least initially) when connected?  Or is it ON and solid (not blinking)?  Or does it no come on at all?

That cable should work with a 4th gen shuffle.  (Just wanted to confirm you do not have a 2nd gen shuffle, or that you bought a USB docking cable that's for 2nd gen shuffle.  And you already said this cable and your shuffle work with the other two computers...)  So, it must be somehow related to the computer with Windows 8.

I don't see the light coming on either.

If the shuffle's light does not come ON at all when you connect it, the shuffle is probably not getting sufficient power from the USB port.  As a test, disconnect all USB devices from the computer.  You can leave standard USB keyboard/mouse connected, if used.  If the computer is a laptop, connect its power adapter so that it's not running on battery power.  Run iTunes and connect shuffle to a direct USB port on the computer, by itself.  Try more than one USB port.  Is there any difference?  Still no light on the shuffle?