Can you see anything faintly on the screen? I have found the menu bar is the easiest to see. You may be able to get the screen to light up if you apply pressure on the left hand side of the screen about midway up (from the back of course).

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No, there's nothing. I shined a light from the back (it wasn't a big light, but strong enough) and there was nothing either.

My head was spinning yesterday from so much reading up about it, so I thought that it might be just the inverter. But it can't be. If the GPU was OK I'd be able to get output on an external monitor and I can't.