I presume it's draining to nothing over a short time? A day or so? Mine does drain down, but over perhaps a week or longer.
Because of this I don't really think that the power switch actually switches the full battery volts but that the switch tells the CPU to start up.... In this case some components will be draining the battery slowly all the time, keeping an eye out for when the switch is... well.... switched!
Is the machine new or second-hand? Either, it could be a dud battery.
Unh.