I would try checking my battery, for it is quite possible that your battery is no good. Not sure how old your computer is but often that does not matter when the battery has been overcharged to many times. Something I found out the hard way after leaving my own on the charger long after the battery had been fully charged. Mine also would not stay on once unplugged. Also the other thing that could be is for some reason the battery is not able to receive a charge. check your charger that it is working properly and if your charger is one that has the needle like connection inside check that it is not bent or damaged and that it is clean inside, because that it is another problem I have encountered. I this helps....goodluck
Will the laptop run on battery alone, once it is turned on?
If the battery is fully charge, but it won't turn on with just the battery, then the battery could be not putting out enough power. This can happen when it is starting to go bad, it will put out less and less power and the device needs a specific amount to run and a specific amount of power to turn on.
Also, you may want to check your power settings. If they are somehow set to make it so that the device won't turn on with battery alone, then this is an easy fix.
1. Go into "Control Panel" and click the "Power Options".
2. Next to the plan that is currently selected click "Change Plan Settings".
3. Now click "Change Advanced Power Settings".
4. Check through the different options listed and make sure none of them are set to hinder your laptop running or starting on battery alone.
5. If any changes are made...click "Apply".
6. Now click "OK"
7. Finally shut down and power up the computer.