Does your fan spin up when the screen goes black? Can you hear the hard drive to rotate?
If you are able to observe the laptop that is working, but there's no signal on your screen, probably the issue is related to your video chip on the mother board. It's called the North Bridge and it's responsible for emiting video signal. May be, if you try to connect it to external monitor you won't be able to see anything there either.
If you are good with laptops you can open it and verify if the so called "paste" has been desoldered.
If you're not sure about what to do, then you can bring it to a professional tech company to do that for you.