|According to a technician who posted here, dropping a laptop (or other physical trauma) , or spilling liquid on it, are the most common things that cause damage to the laptop that often cannot be fixed except by replacing internal pieces.|
If you're SURE you, or whoever else who has access to the computer, have not done either of those, then your symptoms probably have nothing to do with a cracked board or a damaged component inside the case,
although, if the laptop has been opened and closed a lot, the wiring between the display and the video adapter may be damaged, most likely where it passes through the hinge area.
Laptop no video (or video problems), and battery, AC adapter, power jack T shooting.
See response 1:
DO NOT plug in or unplug a monitor's video cable into / from a video port while the computer is running. Doing so can damage the monitor's circuits and/or the video adapter's circuits.
Some laptops will display on an external monitor without you having to do anything.
If you get no video on an external monitor, some laptops have a key combo that you must press to toggle the display to external video only / sometimes both / built in display video only - see the Owner's or User's manual for the model.