I have been fixing electronics, including computers my entire adult life. I have an engineering degree to be able to understand how things work, and why things fail.
That said, your very SPECIFIC combination of symptoms, no. And there is an infinite set I have not seen as well, that does not mean I can't fix them. It's just a matter of if they are worth fixing.
THAT SAID.
It almost sounds like a power switch that is always in the on position. But in computers, that would force it to shutdown again, and restart ad infinitum.
This is NOT a software problem, this is absolutely a hardware problem. Now the question is what hardware?
Has it seen a spill anytime in the past? It sometimes takes a while for the corrosion to create a "circuit" that causes this kind of failure.
You have nothing to lose here, if you don't think it is worth the $ 300-400 APPROXIMATELY a shop will chrge you to change the motherboard.
SO..... watch
THIS VIDEO which will show you how to take apart your computer for further inspection. Often problems are visible, and can lead you to a fix, sometimes simple. No guarantees. Take it apart just far enough to be able to examine the top of the motherboard with the keyboard off. You may need to remove a few other items as well . I would be looking at where the power comes into the mommy board, and really, just a very CLOSE inspection of the MB. (motherboard
) It could be a visible foreign piece of something conductive like a staple, or a invisible dead IC or corrosion. The Idea is to root out any visible issues, for instance a common problem like bad electrolytic capacitors.