Power on issue

Hello everyone,

This is my very first post on this forum. I am facing a very strange issue with a Macbook Air 13" Mid 2012. Before I begin, it is out of warranty.

Here is the problem I'm encountering: when I turn off the computer and after it is completely off, I'm unable to turn it back on again right away*. It refuses to power on no matter what I try. This also happens when it is on and I close the lid and leave it there to sleep for a long period of time (saying around more than 4 hours).

* It seems to turn back on at random times, for example if I leave it there for x amount of hours and try to press the power key again. Also, awkwardly after I turned it off and tried to power it back again to no avail, I left the lid open and after a couple of hours it turned itself back on again (chime sound playing). That happened to me at least twice.

I have tried the following already with no success: SMC reset, NVRAM reset, battery calibration (full cycling), changed system preferences for energy saving settings in all possible ways. When the computer is on and working, everything is fine. No slowdowns, no freezes, no overheating, the fan isn't noisy and the computer is responsive and runs perfectly well. Does anyone have a clue?

Here are the computer's specs:

MacBook Air (13-inch, Mid 2012)

Processor: 1,8GHz Intel core i5

Memory: 4Gb 1600MHz DDR3

Graphics: Intel HD Graphics 4000 1536Mb

OS X El Capitan version 10.11.3

Thank you for your help.