Just sharing the solution to this. Recently I have been searching all posts, forums, and questions/answers on the net. But I have not been able to solve the problem of screen brightness adjustability on my VAIO laptop. Some minutes ago, I updated all
my drivers (Intel) on the official sony website, which is available to all sony users. The problem still persisted.
What really solved the problem is that the NVIDIA graphics was outdated. I have a GT740M, and updated it to 8.11.18.1146 and rebooted. The update is available in VAIO Update (desktop). Now my screen brightness can be adjusted, as I normally did, with
the Fn Key!
Hope this helps other VAIO users. Good Luck!