It could be several possibilities, but based on your description I can't be sure.
Was it dropped or did you spill anything on it? Is it Hot? Did you buy it brand new or used? How old is it? What were you doing right before it shut down? Have you upgraded anything (ram/hard drive, etc)? Any recent (however irrelevant) repairs done? Anything loose (like the jack where you plug in the power plug)? If you take the battery out and plug it in does it still not work? How about with the battery in and the power plug out?
It could be the system board, the lcd screen, the inverter (if it has one separate from the board) or the power jack itself.
Being unresponsive to keyboard (caps lock light not on, etc) it could be the board or the power jack.