To check where the problem is
if the power light is on,then you need to check the fan to see if it dont run, it may be the [http://www.systemboardcn.com/default/new-original-apple-macbook-air-11-a1370-2010-keyboard-topcase.html|A1370 keyboard] or [http://www.systemboardcn.com/default/13-macbook-air-mc503-mc504-a1369-topcase-with-keyboard-no-backlit-no-trackpad-2010.html|A1369 keyboard] , or the logicboard problem
if the power light is not on, it may be the magesafe power DC-IN jack problem
If you want to solve this problem completely,you may as to find a technician