An unresponsive laptop may genuinely be broken, and the following simple steps will help confirm whether it indeed is.
Remove the laptop from any docking station to which it may be connected.
Disconnect all peripherals from the laptop.
Wait until the laptop does not feel warm to the touch.
Test the outlet into which the laptop is plugged. (GFI grounded outlets occasionally “trip,” in which case they no longer supply power.) Upon verifying that the outlet works, plug the laptop into it try turning it on.
If the laptop doesn’t start, remove its power cable and, if possible, its battery as well.
Press and hold the power button for 30 seconds.
After reconnecting its battery and power cable, try turning on the computer again.