Are you shutting the lid before it actually shuts down? If so this will actually cause the computer to go into sleep mode. When you click shut down wait a second or two to actually see the screen start saying "shutting down" and then close your lid.
Like previously said too, if your power cord is connected to the laptop there will be an LED lit to indicate that its charging. But that does not mean its "on".
Hi. I have the same problem too. I just noticed it earlier or maybe the problem started today only. When I shutdown it, then close the lid, after 10 secs. the LED (power) light turns on. The light is red. I don't know what the problem. Please help. This is Toshiba Satellite.