I am running 16.04 LTS and tried to install dropbox caja, but when I clicked on it nothing happened, it also did not start after boot.
So I went to the dropbox website and downloaded dropbox for ubuntu. This works with caja, but you have to start dropbox manually by clicking on it.
Only you. I use Dropbox (which I installed from the website) with no problems.
Maybe is because your first failed installation.
Try uninstalling dropbox and then try to uninstalling from CLI. Then try installing the one from the official site.
I have also installed caja-dropbox after that and it works with ease. Also the daemon works nice.
It is solved. It works with the application downloadable on the Dropbox website.