Thanks for your answer!
My speed is 10/1. I am not, however, uploading 1 Mb/s at all -- I'd rather say 10Kb/min, if at all. I get decent speeds when uploading directly using the dropbox folder in my computer or a browser. It is like this software is the one throttling the upload to Dropbox.
And also, I still don't get why stops the upload every 20/30 minutes. As a result, I cannot really upload during the night, which might be an option to have my files up there before 2014!
Tried uninstalling and reinstalling, again, but nothing happened. Oh well. Any suggestions? Anyone having a similar problem?