I'm using 12.04 with Xfce on a Chromebook using crouton. The package downloads and says it needs to install proprietary software. It seems to finish and then just does nothing. It also does nothing when I try and run Dropbox again. I have just successfully installed on another machine (14.04, Xfce, non-Chromebook) where after installation it shows a GUI window asking me to log-in, which is what I'd expect.
Also if I try running
~/.dropbox-dist/dropboxd a process is started and the terminal remains blank (no errors).
I've also tried a number of workaround methods from similar posts, including downloading from the repo rather than the Dropbox site.