Solved!
(Three full days so far)
Changed the Memory and it seems to have worked!
Setup: iMac 27 Mid 2011, 3.4GHZ, 16GB (Crucial), AMD Radeon HD 6970M 2048MB
I started getting the White Screen about 3 weeks ago, about a week after I upgraded to Mountain Lion.
Right away I suspected the Graphics Card overheating (from my PC Days when this was common), as right before I got the White Screen the screen got pixelated then the screen shifted half way horizontally so that the Apple logo on the menu bar was in the middle of the screen.
But then I started reading this forum and tried everything that had been said here, it would work for a while but then I would get the white screen. I finally opened the computer and found lots of dust on the fans so I cleaned that - Same.
I then read someone somewhere about the memory having been the problem. So I took out my Crucial 16 GB and replaced it with the original 4GB (2x2) and it worked flawlessly for a full day of work.
But because I run Fusion VM Windows 7, the 4GB of which I gave 1.5 GB to the VM this made my whole computer really really slow. So at the end of my work day I figure I would put back 2 Crucial sitcks to narrow down the problem memory. Within minutes my computer froze and the white screen came back.
So back I went to my original 4GB.
Then I noticed my Toshiba Laptop had the same memory sticks my iMac had including the same brand, Samsung so i poached them to the iMac for a total of 12GB.
The 12GB been working fine two days now.
My theory, I think this became an issue as a combination of factors. Mountain Lion must be making my machine run a bit warmer. The fans had lots of dust which was affecting the airflow this led to heat failure on the memory sticks and left them weaker even after i cleaned the fans.
For now, I want to make sure the Samsung Memory works consistently for at least another 3 days then I will swap the 4GB sticks for the other 2 Crucial stick until I find out which one is bad.
Anyway, I figure I contribute back to this forum as many of the ideas here helped me.
I am sure this is not the last word on this subject as it seems there are multiple vectors to this issue at least it is one down.
I was starting to loose faith in Apple, but if it is the memory I added from Crucial then I will take back all the cursing at it.
( I was already doing the math between taking the iMac to Apple Care and pay the piper for a new video card or just buy a 27" HD monitor and go back to my Windows machine.
Please note, I am not blaming the Crucial memory, but rather my fault b/c of the dust in the fans. I had the Crucial memory working flawlessly for about 4 months before this incident.