Hello,
First things first.
I'm assuming you notebook is out of warranty...?
Is your notebook's display CCFL or LED backlit? Also, what is your Sony VAIO laptop model? If there are several variants, provide a specific model/product number. This is important for you to be able to know what you need to replace, and what parts you'll need to buy.
If your laptop has CCFL backlighting, then either a faulty CCFL backlight and/or the inverter may be causing the problem. However, if your laptop has LED backlighting, then only the LED backlight is likely to be causing the problem (since they typically don't require an inverter). I'm unsure of whether the LED backlight can be replaced in an LCD LED backlit display; it is my understanding that the whole display has to be replaced.
Other problems like loose wiring may also be the causing the problem. In any instance, if you're going to repair the notebook yourself, it's best to get hold of a service manual for your notebook (usually obtainable from the manufacturer's support website) to be clear of the innards of your notebook, and the specific parts involved (which you'll likely need to replace).
As already mentioned, replacing notebook parts can be very costly, and end up costing more than the notebook is actually worth. eBay is usually a good place to find cheap replacement parts for notebooks, so once you've identified the part numbers for the parts that need replacing, it might be wise to look there.
