I downloaded PPSSPP version 1.0 and Peace Walker works well. Fullscreen also works. While I suppose I can master the strange Peace Walker control scheme with time I'm not sure I want to devote the time to it and the button controlled camera seems like a minor disaster.
Tried direct3D9 and the game crashed in the same spot.
EDIT: Tried direct3D9 with the most recent version of PPSSPP to be clear.
Were you using the latest build?
You can set the Dpad to 2 places on the controller FYI, put the Dpad on both the Dpad and the right stick, does wonders.
THE BEST METHOD to run PSX games (and everything else for that matter) is via Retroarch - http://buildbot.libretro.com/nightly/
If you have any questions on how to set it up on Windows please feel free to ask, its very easy.