If the splash screen flickers then the game segfaults, before resorting to desperate measures like sudo, try:
MESA_GLSL=dump ./DungeonDefenders
If it reports something like extension `GL_EXT_bindable_uniform' unsupported in fragment shader, you're seeing https://bugzilla.icculus.org/show_bug.cgi?id=5823 . Try using other graphics hardware.
The sed procedure documented in that bug worked pretty well for me to get around that segfault error (I'm on Ubuntu 12.10 running on a 2012 Macbook Air 5,2 w/Intel HD4000 graphics). I can start the game and play local levels after a little bit of stuttering on the startup and loading screens. The graphics look great, frame rate is pretty reasonable at 800x600 pixels, 1440x900 was a bit slow.
So if you're running into that GL_EXT error, give that a whirl before you go buy a new computer to run DD.