I'm having the same issue with my Sony Vaio VPCEG16FM latop. I ended up having to reload the computer with a fresh install and updated the graphics driver to the latest version and it keeps flickering like a strobe light, but the image is still visible. So kind of like the beginning of the original posters video before it blacks out.. I thought it was a connectivity issue at first, so I took it apart to make sure the cable was secure in the back of the screen, but it still did the same thing. After that, I ended up uninstalling the driver to the default "Standard VGA graphics" driver provided by Microsoft and the issue hasn't happened since. The following was taken from the DxDiag:
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System Information
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Time of this report: 7/11/2014, 23:15:23
Operating System: Windows 7 Home Premium 64-bit (6.1, Build 7601) Service Pack 1 (7601.win7sp1_gdr.140303-2144)
System Manufacturer: Sony Corporation
System Model: VPCEG16FM
BIOS: InsydeH2O Version 03.61.04R0220Z8
Processor: Intel(R) Core(TM) i5-2410M CPU @ 2.30GHz (4 CPUs), ~2.3GHz
Memory: 4096MB RAM
Available OS Memory: 4044MB RAM
Page File: 1135MB used, 6950MB available
DirectX Version: DirectX 11
DX Setup Parameters: Not found
User DPI Setting: Using System DPI
System DPI Setting: 96 DPI (100 percent)
DWM DPI Scaling: Disabled
DxDiag Version: 6.01.7601.17514 32bit Unicode
Sorry for the length of all that, I figured the more info I give, the easier it might be to figure out the issue. Please, I am unable to use the laptop at the moment with the latest driver. Without it, it works fine, so I've eliminated the hardware. If any further information is needed, I'll do my best to provide it.