AC adapt. and Battery

I was wondering: can a Laptop can power up if the AC adapter is plugged into it, but the battery is taken out? Usually when the laptop is off and the battery is in, and the adapt. is plugged in, the battery LED light will be on indicating if the battery is fully charged or charging up. However, recently my laptop hasn't been powering up, and so I was looking at the battery LED and the light wasn't on even with the battery and adapt. plugged in. When I press the power button the LED lights will flash once but the Battery light will be orange (either uncharged on not detecting adapt. So is it possible my battery is drained, or is the AC adapt. not working correctly by not supplying juice to the battery?

!---Thanks---!