Hi,
I bought the game on Steam several months ago and when I launch the game from the launcher, I have a white (yes... not black) screen and I have to kill the process manually (no error message). I tried to use the minimal settings but nothing changed.
My hpl.log is really short so I hope you will be able to help me 
Version 1.20
-------- THE HPL ENGINE LOG ------------
Engine build ID 20101021192547
Creating Engine Modules
--------------------------------------------------------
 Creating graphics module
 Creating system module
 Creating resource module
 Creating input module
 Creating sound module
 Creating physics module
 Creating ai module
 Creating gui module
 Creating generate module
 Creating haptic module
 Creating scene module
--------------------------------------------------------
Initializing Resources Module
--------------------------------------------------------
 Creating loader handlers 
 Creating resource managers
 Adding loaders to handlers 
--------------------------------------------------------
Initializing Graphics Module
--------------------------------------------------------
Init lowlevel graphics: 1280x800 bpp:32 fs:0 ms:0 gpufmt:2 cap:'Amnesia - The Dark Descent - Loading...' pos

-1x-1)
 Setting video mode: 1280 x 800 - 32 bpp
And that's all !
The weird thing is that I downloaded and installed a pirated version of the game after that and it works perfectly fine, even with the highest settings ! So I'm totally lost now :'(
My drivers are up to date.
Specs : Windows 7 64 , Radeon HD 7870, intel i5 2500k
If you need the hpl.log from the pirated version i will be glad to post it, if it can help you.
That's a very weird issue oO
Thanks for reading !
edit : i forgot to mention that I deleted the game in the Steam folder and the Documents Folder... nothing changed.