Check that the Power On button is not stuck down in the operated position.
The power button is part of the keyboard assembly and if it "appears" to be permanently operated the laptop won't turn on. Disconnecting the keyboard, disconnects the power button.
If it seems to be OK you may have to replace the keyboard.
Here's the hardware maintenance manual for the laptop. Go to p.34 to see how to remove/replace the keyboard.
Here's a link to the parts for the laptop. Click on Select Commodity > Keyboards Internals (19) to find the part numbers for all the keyboards available for the model. Usually the part number can be found somewhere on the underside of the keyboard if you wish to verify that you're getting the same one.
Search online using the part number only to find suppliers that suit you best.