MacBook turns off on its own but when booted back resumes @ that point

There has been discussions and solutions to a slightly similar case where the screen goes black suddenly(keyboard back lights still on), fans go crazy for few seconds and then macbook shuts down.

But, my case is different! All of a sudden the screen turns off (it's different from "going black), keyboard back lights go off, the trackpad won't work (there is no feedback/click feel).

When I boot up: sometimes even before the bar below Apple logo gets filled, it turns off again. If it does complete the booting process, I see everything where it was left. Movie is paused at the moment just before turning off. Browser has the tabs open, but I have to reload them. I don't have any application added as a login item.

What's weird is that this "Turn off process" can't be technically termed as a "shut down" because if a system is shut down, all the applications are closed before powering off and they don't simply pop up when powered on (when no app is selected as a login item).

If I take it to an authorised service centre they say I just have to replace the logic board. If they run a hardware check everything is reported as normal.

Please help me resolve or atleast understand this issue.