Shania Sharma :
Unfortunately I'm going through the same problem. A few days ago my laptop (x550l) shut off and gave me a heart attack when it wouldn't respond. I waited a few hours, removed the battery (blew on it like a GameCube) and inserted it and pressed the power button, and it turned on- for about 10 minutes. After that it shut off again and still hasn't responded to anything. It doesn't seem like it's charging, the LED doesn't light up over the battery symbol. I tried holding the power button for what felt like ages, to no avail.
Shania, what you need to do is turn off your laptop, (make sure it's also unplugged from the AC power brick), then remove the battery, THEN press the power button and hold it down for about 30 seconds. This will dissipate whatever residual charge is on the system board.
THEN plug the AC power cord back into your laptop, and turn it on with the power button. Your laptop should start right up, normally.
Once that's done, then power down the laptop again, unplug it, then re-install the battery again, then plug it back into the AC power brick, and you're good to go.
Just remember to do it this way, if this ever happens again.
The problem is, the system board ("motherboard") gets charged up with residual charge (electrostatic), and it needs to discharge it somehow. This procedure will do just that.