battery - Asus laptop won't turn on

I think I ran the battery too low (I have one power cord that I share between two computers and I was stupidly trying to use both machines at the same time and lost track of how long this one had been unplugged). This is an Asus X44H, and now it won't power on. I tried removing the battery and holding down the power button for several minutes, but when I put the battery back in, it didn't turn on; the only sign of power I get is that the green light next to the light bulb symbol is turned on. I've tried leaving the computer plugged in for three or four hours, but so far nothing happens other than this green light's staying on. Is leaving the machine plugged in, say, overnight likely to help? Or is there something else I can do that could get this to power on again? Thanks.