Power up problem

Hey guys

I woke up today to power up my laptop, but for some reason, it failed.
The power button didn't show the usual light it shows when it's on.
I removed the battery, unplugged my laptop, held down the power button for 30 seconds, plugged my charger, nothing happened, still couldn't turn it on. (Used an online guide to do that).
After I kept the battery out of the laptop for about 15 minutes, I put it back in and the laptop started by itself (yes, weird).
Out of curiosity, I wanted to see if I managed to fix my problem, so I shut down my system, and it actually restarted instead of shutting down. I couldn't get it to shutdown.
I pressed the power button to shut it down, and after that, I couldn't get it to start up again.
I repeated the first procedure I did (left battery out for 15 minutes), and now I'm here, scared of shutting down my laptop again.

What might be causing this?
Is it a hardware or a software problem? (Or both?)
What can I do to fix it?

 

Hi, TripleR. Welcome to Major Geeks.

Could you please tell us the make and model of the laptop? What version of Windows are you running including Service Pack?

 

Thank you mdonah

My laptop is an HP Pavilion G6/2258ee
I'm running Windows 8.1 64 bit (upgraded from Windows 8)
(Also running Ubuntu 14.04 but rarely use it)

http://i57.tinypic.com/ivlqpe.png