I initially thought the problem was my laptop charger however I just put a new one in and I am having the same problem. Whenever the power button is pressed to turn on the laptop the charger light which says its charging off and the computer doesn't turn on. My computer is also fairly old and its time may have just come :( Thanks for your help in advance anyway :)
If you change the charger and the issue still exists, this means that the charger is not appropriate for your laptop. Check out the output voltages if they are in accordance with the battery.
I suggest you to change your charger according the real voltage of your laptop.