Do the following and it should allow you to charge the battery again. If, however, after even fully charging it still won't start the laptop, only run it after it is already started, then you are either going to always start when attached to the cord or get a new battery.
Try the following and see if it will turn on.
1. First make sure the device has been charged.
2. Unplug your charger cord.
3. Remove the battery.
4. Press and hold the "Power" button for 30 seconds and see if the device will turn on.
5. 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...