|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.
If you don't mind using an external monitor with your laptop, then there are also video adapters you can connect to a laptop that you can connect an external monitor to.
E.g. see this older subject, although some links in it may no longer work: