Something seen on first look, You had denied write access to your Dropbox Directory (mode=0o40555 uid=0 gid=0 - have to be mode=0o40777 uid=0 gid=0 for everything). Is there some reason? Dropbox can't work is such a case. Probably you had done this unintentionally. Go in your Dropbox folder preferences (in the explorer) and remove every 'Deny' check marks there. This is enough least as a first step.
Let's hope this will do the trick for you.
PS: As an alternative, if you can get in your Dropbox preferences, turn to 'Account' tab, click somwhere inside (doesn't matter where exacly - just some empty place in tab area) push space key or option key and push 'Fix Permissions' button, which just popped out. If you can't get in the application GUI, alternative could be the following command in a terminal: