It's funny how things work.

I switched the battery for the original one, the one I discarded because it had some problem in the internal logic (sometimes it lasted for a day, sometimes for half an our).

Everything was exactly as you detailed, so the problem had to be with my Mugen's battery.

Then, I switched batteries again and now, the one from Mugen's behaves exactly as you described. The problem is gone.

I don't know what it was (you saw the video) but the good thing is now I know how to revert it if it happens again: I just have to reboot with the original battery.

Thanks.