Hmm, since the screen still has a faint "glow", I'm thinking it is a driver fault, though it also could be a loose cable connection (though loose cable connections tend to give a slightly different behavior than this).
Nearly a year? That's critical. I've had my L1020 for "nearly a year" when it broke down, but that was 10 months from the date of purchase so it was still covered by warranty. If your phone has been with you for less than 12 months, chances are that the warranty is still valid.
At any rate, it looks like that the phone has to be opened anyway, so the best method would be by taking your phone to a service center, hopefully with a valid warranty.