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There is a standard set of troubleshooting steps you can take for this sort of problem. So let's go through those first and see if it helps.
If the battery is removable, remove the battery. Unplug the machine from AC power. Then press and hold the power button for at least 20 seconds. Then attach only AC power – of course of the battery is in removable it will still be in there and then try turning the system on. If it doesn't come up after this then the hardware failure is most likely with the motherboard or the hard drive but we were testing with that procedure was whether or not the problem is with the power supply or with the battery. The battery's most common problem and once they fail sometimes the systems cannot run even if they're plugged in as long as the battery is in.