OK now it is more complex as it will entail looking inside the computer and reseating all the components and clearing out any dust bunnies
While you are thinking about that we will power drain the computer
1.Disconnect all peripheral devices and remove all USB devices and media cards. You want to test the computer not the accessories!
2.Disconnect the AC power adapter, remove the battery, and then press and hold the power button for at least 15 seconds .
3.Reconnect the AC power adapter (but do not connect the battery), Press the Power button, Look for glowing LEDs near caps lock and num lock keys, and Listen for sounds of a disk drive and fan turning.
4.If that looks good then insert the battery and try a normal boot