First try testing the power cord to see if that is the issue. If not that, try the battery. You may also want to try running it with the cord only, and the battery out. If neither the battery nor the cord turns out to be the problem, then you are looking at hardware issues. Depending on how much you know about computers, you can either do the work yourself, or take it to someone.
NOTE: If your device is under warranty still, do not let anyone work on it until after you contact the manufacturer, as doing so would void the warranty.