I'm afraid it'll be pretty hard to solve the problem without any logs or errors. Only basic things: Check your Java version (must be 1.7+). Check that dbeaver version matches your OS and your Java (32-64 bit).
If you upgraded some previous version using deb installer - try to remove this previous dbeaver installation completely (rm -rf /usr/share/dbeaver) and reinstall again. Another way - download zip archive and extract it in some folder in your home.
Success! Removing ~/.dbeaver before the new install did it. It doesn't seem that even 'purge'ing the old installation with dpkg touched that directory.