Is the laptop fully charged? If not do this as a first step.
Have you tried pressing the power-on button and holding it on for 30 seconds?
Have you tried holding down Fn and 8 keys?
Try powering up the machine will tapping the F2 key - a menu should pop up - go to power management and set to default.
If no luck try a hard reset
Disconnect the power lead from laptop and power socket- remove the battery - press the power button for 30 seconds -plug the power lead back in - press the power button - it should re-boot and power off and then restart - replace the battery.
If this is successful you need to have a look at the power settings.