Laptop shuts down with a click sound [NOT OVERHEAT]

Hello,
I have a TOSHIBA satellite p850 running on windows 8.

Three days ago, my laptop suddenly shuts itself down without any warning notice, just a click sound.

When i tried to turn it on again, it shows the toshiba logo for 10sec and shuts downs again. In some occasions it gets into the login page, after i entered the password and few seconds during desktop startup, it shuts down again.

Then, i refreshed my windows and the problem was gone, or so i thought. The problem came back that night, i suspected overheating and i opened the fan and cleaned the heatsink, but problem still persist.

i suspected the battery or AC power adapter is causing the problem (because my battery is in a bad health, and my AC power adapter is charging poorly as well). I tried turning it on with just battery attached, still shuts down itself. I tried turning it on with just AC power adapter plugged in, still shuts down itself.

I tried starting in safe mode it still shuts down. I tried hard reset, does not fix it. i tried manually shut down the laptop using shutdown /s /t 0, no avail.

I looked online, some say it could be motherboard problem but if it really is, can i even reach the desktop startup? It feels like software problem to me because it can stay at the login page for quite some time without shutting down (if i dont enter the password).

Any help would be greatly appreciated as my dissertation is due in 8 days!