Is the computer turning on when its plugged in to the wall? If not, take the battery out of the laptop, and see if it turns on while plugged in with no battery. If it still doesn't work, then it could be your charger is bad, or it will be a problem with the charging port on the laptop, or a problem with the motherboard. A dead battery shouldn't stop the computer from turning on unless its also causing a short circuit which is not very common.
If you brought this into my shop, the first thing I would do is test a new charger. If you don't have one, see if there's a local computer repair shop nearby where they can plug in one of their chargers for you.