Restarting after shutdown(run out of power)

Question

Device:
MacBook Pro - non Retina disp
13" - Mid 2012
2.9 GHz intel.C i7
8GB RAM
Greetings all,
So I've purchased my mac earlier this year and approximately after a month I've been noticing this weird thing happening whenever i re-use it in low power.
So I'm using my device until the battery power reaches a low percentage (around 10% and lower) and then i close the lid (Mac goes to sleep), and leave it for  some time (sometimes from night to morning and others for just couple of hours). then when i come back to use it, it doesn't start whenever i push the power button (no power). i then plug in the power cable and wait:
- sometimes 5, 10, 30, 50 seconds
-sometimes 1,2,4,5,10 minutes
-and sometimes more than half an hour!.
and then press the power button again. now, it does work and here is where the weird thing is happening.
once i press the power button, the screen becomes all grey and behind it is my log-in picture background with the log in password box. right beneath it there is a loading bar. it doesn't show me any loading process*. it just appears fully loaded (all bars are colored).
then it suddenly shuts down. i press multiple keyboard buttons, mouse and it doesn't respond. only sometimes when it shuts down there is light from the screen (black), but the very most of the times the devise "looks" completely shutdown.
i then press the power button again and everything goes normal, except that its slow when i type my log-in password.
once or twice the grey screen appeared again(2 times).
I've videoed the whole thing: https://www.youtube.com/watch?v=MHsmNaYBWns
* The video shows loading process, but it doesn't usually happen.

Answer 1

I managed to start it again, I just had to wait a while (battery power was too weak).