As against what TDX wrote, I think that's answered by your first post: that the screen went 'all white' when the video signal was removed. Bushy's 'connector' diagnosis is much more likely. Since it sounds as tho' you are acquainted with removing the ribbon connector, it's worth trawling for a replacement one. Don't know about the Vaio, but I've replaced a couple (obtained via Ebay) in the last year which solved signal problems... tho this was complete (or intermittent) loss of signal altogether.
Good luck.