I have UE 4.0.2 installed but it won’t let me attempt to open my project in that engine version, at least through the graphical interface.
I found that I was able to finally get into the project by editing the DefaultEngine.ini and pointing the EditorDefaultMap setting to a bare bones example map. It turned out that all of my assets and the project file itself were fine, but the most recent iteration of the game’s (only) map was causing the crash. Reverting to an autosave meant I only lost about 1.5 hours of work in the end (whew!!).
If it helps, all I can recall doing in the map since that autosave was organizing the level’s actors into folders and creating a new post effects volume with a blendable attached. I might have also changed the staticity of a couple directional lights.