I have heard that when this happens that there is either a problem with your AC adaptor or the AC jack on your laptop, but it's most likely the AC adaptor.
What you can do is Remove the battery and then hold the power button for 10 seconds, then try again with the battery. You can also try to do this and then try to start it without the battery in the laptop. The last thing you can do is just get another AC adaptor this should resolve the issue. Also check that the fans can spin freely and are not blocked/clogged. But if none of these methods work then it's probably something inside the laptop causing a short (screw, bug, anything small) inside on the motherboard OR your AC port has seen the best of life. You could try to have the AC port repaired, but have all other parts checked out first (might be a faulty part as well).