Xbox One turning on and off after changing thermal paste

Some friend told me that his Xbox one was overheating while playing games, sometimes even the console changed suddenly the resolution or turned itself off while playing. Besides, the HDD was damaged so I changed it and reformat a new one with the Xbox's partition system (using this guide).

I opened the console (I already have some experience cleaning computers and consoles), then cleaned it with an air compressor and changed the thermal paste (applying the same amount of thermal paste as in this tutorial). After that, I closed the console and tried to turn it on, but when it turns on (heard the beep sound) after 4 or 7 seconds it turns off itself (again heard the beep from shutting down). No imagen, no fan spinning... just turns on and then turns off after a few secs (just like in this video). I'm pretty sure that is not a PSU issue because I tested the PSU into another console, and it was working fine. Also, I tried that other PSU in my friend's Xbox and it keeps doing the same.

I tried to reopen and change the thermal paste to solve that issue, but the console still shutting on and off by itself. Moreover, the fan shows a kick when it tries to turn on, but never start to spin correctly, just that little kicks. One more time, I decided to open the console and check things... first I made sure that the fan was really working properly, hence I removed the heatsink and left connected only: fan, HDD and the front board that has the power button (without the ribbon cable); surprisingly, the fan was well working but the console was shutting down by itself again, but this time within 4 o 5 secs (I think it happens because the GPU gets warm). So, the fan is not the problem.

The next try was to test the heatsink without the fan, and it goes warm really faster, after two or three attempts to turn on the console, I felt how warm was the heatsink (not sure if that is normal). I think that the heatsink could be damage as well, but it sounds not that easy to occurs. But for now, is my only shot because it appears that the board tries to init, but with the heatsink not working properly, the warm accumulates faster and before sending the turn on signal for the fan, the temperature sensor shuts down the Xbox.

Another possible try (but not the same problem, because that Xbox did not emit sounds when it turns off) is shown in this video, where the main board was cleaned (kind of scary thing the procedure), after that the man uses a heat gun over the GPU and finally (want to think so) he applied thermal paste and close the console. But I'm not really sure that this will works, because I tried with my heat gun at 300° but just for one minute over the GPU... think it requires more temperature and more time, but not pretty sure if is worth it to try.

So, my dear friends... Any suggestions or solutions? It will be really appreciated!