So, my father came to me with his Acer Apire 5536 laptop and said that it wouldn't boot anymore; the screen was just black. At first I tried attaching an external display via the HDMI port and playing with the Fn-F5 and Fn-F6 key combinations. Nothing worked.
Then I turned to Google search and found a lot of stuff about the same problem with may solutions pointing to either fried GPU or dead BIOS battery. Changing the GPU was a rather expensive and/or difficult task, so I looked into changing the BIOS battery as it was a common CR2032 one.
This was inspired after reading this post on Notebook Review's forum. To get to the battery was not as easy as I thought. You pretty much have to tear the laptop apart, but luckily there's a service manual to follow.
So follow the disambly steps in the service manual until you can get to the BIOS battery; put in a new one; and then reverse assemble the laptop again. In my case: Viola!!! the laptop booted into the operating system and my father was happy.