Why my laptop not powering / turning on when plugged in?

Before this problem happens, my laptop gives an indication three weeks back that the battery life is already low and there was an option to extend battery life which I selected. The laptop was working fine. Yesterday while I tried working on my laptop, it was on the standby mood then I hit the enter key to turn back the screen so i can log in then i was able to do so. After a few hours working, suddenly it hangs up and tried pressing all the possible keys but the cursor not moving so I turn it off using the power on/ off button as i could not shut it down since the cursor is not moving (this is which I always normally do whenever my laptop hangs up, then power it on again). But this time when i did the same way and tried to power it on, it does not turn on. I connect the power plugged in but the power light indicator lights for a second then went off. I press the power button on/off but nothing is happening. Kindly tell me what should I do?