Firstly, check you can upload using the HTML or Flash uploader.
Next, switch Web Inspector and see if there are any client-side JavaScript errors being thrown. You can also check the alfresco.log file for error on the server (or look at the Tomcat console window, as they'll appear there too).
Try creating an new subfolder and see if you can drag-and-drop into that?
Otherwise you'll have to go into more detail about how you created the site, and exactly what action you're taking and how it fails.
Thanks,
Mike