Some viruses are very very bad and will actually execute with a PC that is shut off. If it detects it's off, it plugs itself into the outlet and turns itself on - but it runs silently by turning the fans off and the lights off (like the power LED). Then it begins executing a lot of code really quickly and the CPU burns up because the fans are disabled. If there is internet access, it also emails your passwords to all your contacts.
True story.
Yeah, this happened to me too! And my PC was unplugged! As I understand it, the virus is transmitted via ultraviolet light waves that penetrate the hard drive and go directly to the Windows kernel. The same ultraviolet light also activates the power supply, which charges up just long enough to send all your porn and passwords out to your contacts and to black hatters!
No.