Was it particularly it when it shut down for the last time? My old laptop died about a year ago very suddenly, never turned on again much like yours. It was pretty hot, and had a tendency to shut down from time to time I assume due to excessive heat. (Couldn't always cool itself sufficiently I guess)
If it was a heat problem, a chip could have died. That could be pretty bad, but there are some repair shops that can change chips out there.
I'd guess that a loose power brick connector wouldn't have gone down so suddenly. It'd have given you a plug me in warning as the battery went down, and you'd have noticed that it didn't recognize the power cord. And it should have tried to turn on for a moment but then give you a critical battery indicator of some kind and not come fully on, and go back off.
In my case, there is a possibility of a short, as when I started looking, I realized that one of the battery lock clips had dislodged and vanished inside, so there's probably a spring wandering around in there... Someday I'll crack it wide open and look around further, and I plan to do some serious laptop repair learning soon, but for now I'm kindof guessing.
