If you tried turning it on with the charger connected but the battery disconnected, then the issue likely isn't the battery but rather the computer's hardware. I will include info for both battery and hardware anyways. Particularly because a laptop frying its power management simply because it discharged, would be odd. Try them in this order.
Computer: With the battery and power adapter disconnected, push and hold the power button for 15 seconds. This removes residual power from the device. I've seen this trick work on many systems experiencing the same issue you're describing.
Battery: It is possible to jump start a li-ion battery. This usually only works if the battery was left unattended for long periods of time and rarely works. I recommend first checking the voltage of the battery with a multimeter. If it doesn't have any voltage, you're a good candidate. If you don't have a multimeter, you can still jump it, but should take precaution.
You can take a 9v battery or another laptop battery and connect positive to positive, negative to negative. You should only do this for 1-2 seconds, disconnect and test for functionality. Leaving the battery connected can result in overcharging, bulging, leaking, explosion.
Good luck.