|Have you, or is it possible someone else who had access to this computer...|
- dropped it, or dropped anything on it, or otherwise exposed it to a physical jolt ?
- spilled liquid on it, or sprayed it with liquid, or exposed it to liquid such as rain ?
Since the computer last worked properly all the time, has there been a power failure event that happened while the AC adapter was plugged in ?
Those things are the most frequent reasons something inside the laptop has been damaged.
The battery can develop internal shorts, especially when it's more than two years old.
Try removing the battery and see if it will run with only the AC adapter connected to it.
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 / built in display video only / sometimes both - see the Owner's or User's manual for the model.