@Mary Kay,
Like I said, it's all pretty much guesswork since we can't get our hands on the computer over the net. But here are my guesses:
In theory, the light you are talking about might not indicate that the laptop is powered up, and may just indicate that it is connected to a powered source (but not going past the battery) in practice I don't know how common that is, but it could still be a bad battery.
Broken screen. Screens are the next most common thing I see that breaks on a laptop. You can test this by connecting it to another monitor.
Software: if the screen actually powers up, but is black, it could be that the OS isn't loading, booting off a CD of an operating system is a way to test that.
But it could be a variety of other hardware failures that I can't rule out.