I've just tried to boot my newish Inspiron 5100 and I got what I thought was a black screen. On closer inspection, I can just see the outline of the startup windows, but the screen is very, very dark.
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Attach an external monitor to the VGA port on the back of the system. Then using the Fn-F8 key combination, toggle the video signal to the external monitor and see if the display is good on the external monitor. Check if the same problem appears on the external monitor. If you have an intermittent problem, then you need to use this configuration until the problem appears.
If the problem does not appear on the external monitor, then contact Technical Support.