Well, sorry to hear the 'Quick Fix' didn't work for you.
I assume that it is totally out of warranty so you will have to contact Sony about service.
And it could be something else other than the Sony DSC-S40 white/blank LCD screen curse.
Make sure you take the batteries out before trying my 'Quick Fix' again and make sure the batteries you put back in the camera are new.
1. Hold camera firmly in left hand.
2. Smartly rap front of camera with knuckles of right hand on the "Cyber-shot" logo.
Let me know if this has helped.
The Allens of Allentown, PA USA