dropbox link to their site does not work in contextual menu nor in menu bar
Have you tried downloading the latest version of the Dropbox software (which can be found here: https://www.dropbox.com/install) and reinstalling on your Mac? 

To do this: 


Quit Dropbox from the menubar application
Download the software from the Dropbox website. 
Open the DMG file that gets downloaded 
Double-click the "Install Dropbox" icon in the DMG file 
Follow the instructions to reinstall Dropbox.