Write permission fail
Sometimes the game might crash because of bad file permissions. To fix this, run as Administrator (Windows Vista, 7 & 8.x) or set so the Penumbra executables have write permission on the install directory.
Bad game caches
It might be that some of the game cache files are corrupted. Uninstall the game, then reinstall and see if that helps.
On Steam its possible to verify the game cache directly.
Turn off post effects
Go to Options > Graphics and here you can turn on/off all of the different effects in the game. No restart of the game is needed for these changes, so simple go back to game and see if it has been fixed.
Turn off SSAO
Turn off SSAO in the launcher and see if that helps. It is known that some cards can freeze when rendering SSAO, meaning the game would get stuck after the first logos and text (when menu is supposed to show).