I will break your post down so it is more manageable;
I tried to turn on the laptop and the power button flashes blue for a second and then nothing.
Can you at any time hear the CPU fan working.
Have you tried removing the battery and using only the AC adapter to power the system.
The system specs list it as having two sticks of Ram, if so please remove both sticks of Ram, blow out the slots and then insert only one stick of Ram in slot one and see if the system will boot, if no joy then try the same stick of Ram in slot two and again see if the system will boot up, repeat the procedure with the second stick of Ram.
Let us know the results of the testing.
I know it is not the screen because the first thing I did was try to connect it to an external monitor
Did you press the Fn and external display keys down together to toggle between screens.
I have read that the Video chip caused it. Took laptop apart,took soldering iron and applied heat to the chip. Went back and forth several times until whole chip was hot.
I am not sure what this is intended to achieve.
I put thermal paste on both sides of a penny and used it as a heatsink.Put it back together and still have the same issue.
Sorry but this is asking for trouble, there should be nothing inside your system that does not belong there and especially a loose electrical conducting coin, if the system was to power up the thermal paste would soften and this could lead to the coin ending up on the MB and shorting the whole system out.