Dell N5010 display turns off automatically.

I have a Dell Inspiron N5010. Its graphics card failed a while ago and I had it reflown. Now, much of the problem seems to have gone. However, while I am working, the display goes off automatically, there is no error message or log. I have found out that it returns as if nothing had happened when I apply firm pressure on the area of keys S,W,E on the keyboard registering a couple degrees drop on processor and GPU temperatures in speedfan. The problem most likely is not overheating unless my sensors are malfunctioning. It is sometimes very frequent and sometimes I need to shut it down by pressing power button.

Also, when It has been shut down or put to sleep, it doesn't start again. When I try Fn+power button, it gives 7 beeps warning. It takes a lot of tries and pressure on the said area to get my machine working. 

Does this mean something is loose inside and could be fixed with capable hands?

I opened it up a few days ago and could not find anything wrong. I cleaned the fans and assembled it back on. The thermal paste is fine but I noticed that the part where the heat sink branches and has screw no. 4 had a spongy thing, maybe a foam draped in thermal paste below it. 

Is that thing a part of the design to connect a chip to sink or did someone replace something better or absent with this sponge for improvisation? 

Any help or suggestion will be much appreciated. Thanks in advance!