Try the following and see if it will turn on.
1. Unplug your charger cord.
2. Remove the battery.
3. Press and hold the "Power" button for 30 seconds and see if the device will turn on.
4. If it does, great, if not yet, no big deal. Now plug back in the power/charger cord. (If it didn't turn on without the cord in, it should turn on once you it is in. Yes sometimes they will turn on, or try to turn on, even with nothing attached/plugged in.)
5. Now put the battery back in.
Now see if the batter will charge.
If that doesn't help, try charging the battery with the laptop off. If it will charge when it is off, but not when it is on, then the problem isn't the battery but your charger cord. There is no fix for that, it would just have to...