Isn't there a switch that you can flip in the back?
I know on the PS3 there are two power switches...the touch sensor in the front that when off is in a standby mode, and then the switch in the back which completely kills power to the console as a whole.
Usually I just hold on to the stand-by mode button until it resets manually (though sometimes this will just force it into standby mode). Either way, I think the Xbox360 is the same where you can just hold the front button and it will force a reset without having to completely kill the power, and if there is a power switch on the back, unplugging it is just completely unnecessary and dangerous. As a last resort, always use the kill switch. There should never be a need to unplug it. If you really need to unplug it to continue playing, you might want to send that in for service because at that point, it's not the game, it's your console.
I keep tapping the front switch till it goes off. Sometimes it takes 10+ till the green light goes off. It gets locked up and needs 30 seconds to be able to turn off.