For several months I have had a vertical line across my screen. I have checked whether the driver for the graphics card, NVIDIA GeForce GT 330M is up to tdate. The computer says that the driver is up to date.
This will depend if the problem is caused by software (driver) or a hardware fault (broken wire or poor contact).
Does this happen in BOTH Speed and Stamina modes?
Try connecting an external monitor. Is the fault viewable on a separate monitor?
When you start the Vaio, tap F2 repeatedly when you see the Vaio Logo. This will open the BIOS screens. Is the fault visible in the BIOS Screens?
When starting the Vaio, press F8 repeatedly. Choose Safe Mode. Is the fault visible in Safe Mode?
If the fault is there in the BIOS screens, it will not be the driver which has not yet loaded and you will have a hardware problem that will need someone to look inside for a fault.
If the fault appears on an external monitor then it is probably the driver. Try uninstalling the graphics driver and rebooting to reinstall it. Your Vaio has a Hybrid Driver and there is no update available.