Did you set up your dropbox all at once? Like did you sign up online and download your folder in one session, or did you do them on separate days? The fact that you were taken to a completely different site makes me worry that somehow a "fake" dropbox account was somehow introduced to your computer. There are phishing sites that look similar to real ones, but they are fake. You have to really check the web address, and the publisher and make sure you have the correct one.
Dropbox is: https://www.dropbox.com (Note the https -- that's important. If you think you're on dropbox's site and that "s" isn't there...you're not on the real site.)
Since you don't have any files to lose -- or if you do, make sure you get them out of your computer's dropbox folder and put them somewhere else on your computer. Then, I'd uninstall anything related to dropbox and start from scratch, making sure you go to the proper dropbox website. Then when you sign up again, make sure you have the time to complete all the steps at one time -- sign up, download the folder, etc.
Let us know how it goes!