Laptop on, shine a flashlight at the LCD screen at various angles.
If you see a faint image the problem is the Backlight, or screen Inverter.
90 PERCENT OF THE TIME the fault can be attributed to a bad screen Inverter.
(IF the laptop uses a screen Inverter.
CCFL backlighting uses a screen Inverter.
LED backlighting may, or may Not use a screen Inverter)
No faint images?
See if the problem is the graphics chipset, or Video Cable, or inside the Display Assembly.
Laptop OFF, monitor OFF, connect a VGA monitor to the VGA port, on the laptop.
This is an example of a VGA Cable, and VGA connector, (port),http://en.wikipedia.org/wiki/VGA_Connector
Scroll down a little for cable example.
You can use a CRT type of monitor, (Looks like a small TV), or a flat LCD screen monitor if it has a VGA cable.
Turn the monitor on. If a CRT type of monitor allow it to warm up.
Turn the laptop on.
By factory default settings, the display should show on the external VGA monitor.
There are at least 3 display options available;
1) Internal monitor of laptop ONLY
2) Internal monitor of laptop AND external VGA monitor
3) External VGA monitor ONLY
Hold the Fn key down, and at the same time tap once on the F8 key. (The F8 key is the Display Toggle-Over key)
Still no display on external VGA monitor?
Hold the Fn key down again, and tap once more on the F8 key.
No display on external monitor, suggests a problem with the graphics chipset.
Most of the time the graphics chipset itself isn't the problem.
It is due to inadequate cooling for the graphics chipset, and this causes a problem with the MOUNTING, of the graphics chipset TO motherboard. (BGA surface mount)
If this is found to be the problem I will go into more detail.
I don't believe that is your problem, but there is NO guessing here.
We are following a diagnostic flowchart.
Good graphics on the external VGA monitor, means there is a problem with the Video Cable, or inside the Display Assembly.
A) Video Cable connections can be loose.
Connection at motherboard side, or connection of small cable to screen Inverter from Video Cable, (IF it uses a screen Inverter), or connection at back of LCD screen.
A LOT of times a loose connection can cause what you are seeing.
Video Cable could be damaged. Wires inside stretched/broken.
Inside the Display Assembly:
Video Cable checks out after a continuity test, then the screen Inverter is next in the diagnosis. (IF a screen Inverter is used)
Screen Inverter proves to be good, the problem is the LCD screen.
NO screen Inverter is used, the problem is the LCD screen.
Sony drives me crazy with their model numbering system.
What is the other model number on the bottom of the laptop?
Start with a VGN?
Post back in a Comment.
Once I have a model number I can deal with, I will post back with step by step info, and additional manual information.
(Service Manual. Perhaps pictorial guides, and video/s)
[Chip and Chipset are slang terms for I.C.
The I.C., or chipset for graphics, is the graphics chipset; or more properly known as the G.P.U.
Graphics Processing Unit,http://en.wikipedia.org/wiki/GPU