Bad Monitor or Power plug?

Alright, I have an HP w19 Monitor with a nonstock power plug (the power plug has a little box in the cord as if its a converter). Well anyways if I were to leave my monitor unplugged or leave it off for a very long time and try to turn it on the monitor will turn on just fine, just don't turn it off, it could sleep. If you do turn it off or unplug it then plug it back in you need wait a long time and the little green light blinks and the backlight seems to turn on, maybe for a millisecond or so its really fast, my parents are unable to see the flash. It keeps doing it.

Any hint on what the problem is, maybe a bad capacitor that I might need to resolder in or what I'm hoping, the power plug.

I know its a tough question but any feedback would be great.

btw the monitor in my post is not the monitor, that is my primary monitor, I'm trying to set up duals.