When I am trying to shut down skype

They need to learn that "close" does not mean "minimize." It means CLOSE

Start: control panel: add or remove programs: uninstall

tools>options>advanced>uncheck "keep skype in taskbar while i'm signed in"
you're welcome

Or right click when it is on your task bar it says Quit Skype click it an then just click yes and then your done...until you turn the computer back on.

I laughed too hard at this