It could be the calibre splash logo that's doing it. I had a similar issue with the calibre 2.0 betas on a virtual Mint 15 (Xfce) installation before. The installation would go OK, but it wouldn't run.
Find the gui.json file in calibre's config directory (probably ~/.config/calibre) and look for:
Code:
"show_splash_screen": true,
and change it to:
Code:
"show_splash_screen": false,
Worth a shot anyway.
I have no issues at all with calibre 2.x on Mint 16/Cinnamon, for what it's worth.