I would first try and reseat the connectors for the LCD and Digitizer. If they popped loose or have any corrosion sometimes that will be an easy fix. Unplug the battery, Remove the plate holding them down and reseat. Check for corrosion or burnt or damaged pins while your in there. But unless its gotten wet, you should be okay. Once you plug them back in, plug the battery back in and see if it kicks on.
If it does, close it back up and your ready to rock and roll.
If it doesn't, you may have a bad LCD or Damage to the mainboard.
Also, if it kicks on with the apple logo but then the back light shuts off a split second later, that's usually the indicator of a bad LCD. Replacing the front screen assembly should resolve this.