Screen went black after battery got low

It sounds like your computer automatically went into hibernate mode when the battery got real low, and you couldn't get it out of hibernate. If you disable auto-hibernation, you will eliminate this from happening in the future. Keep in mind that by disabling auto-hibernation, when the battery runs out the computer will just "crash" - it will simply turn off if there is no power. The good thing is, it won't be stuck in hibernate mode, because it never went into hibernate. But you will lose anything you were working on and didn't save before the computer ran out of power. To disable auto-hibernation, go into Control Panel and change your power options.

There is also a power option which will turn the display off when the battery gets down to a certain amount of charge. You can change that option to keep the display on as long as there is any power at all in the battery. Or you could change it to where it dims the screen rather than turning it off when the battery is run down almost all the way.