What model laptop is it? There are several laptops that are known for this type of issue, some HP models especially. Basically, the motherboard and/or the video chip dies.
I seem to have an issue similar to this. The laptop works fine with no issues when connected to an external monitor. The laptop screen powers up and will flash but the picture will not come up. I have checked that it is not set to external screen only. It's an HP Elitebook 6930p.
Any help would be appreciated.