A couple of things to try:
-Leave it connected to the Power for an hour and then try power it on
-Remove the battery, Connect power and try to power on
If you have spare parts or someone with the same laptop try:
-Swap charger cable out with one you know works and then try power on
-Swap battery and try power on
Does the laptop show a flashing light indicating that the power is low or is it another light?
Try and explain the issue a bit more, Is there any strange noises or anything that flashes on the screen, What light flashes and is possible a picture of the light.