Hi,
Since the drap and drop feature in webparts works under Personalization mechanism, you should set the "Enabled" property of Personalization to ture.
I know "cause so many problem" you mentioned means that it needs support from authentication mechanism and it needs database for data storage support. Right now, for the first sector, you may use Anonymous Personalization Trick in Web Parts to handle that, more information, see http://www.codeproject.com/aspnet/anonywebparts.asp
Or, if you just want the feature of Drag and Drop, you may use Altas instead of WebParts, more information, see
How Do I: Use the ASP.NET AJAX Draggable Panel Extender? http://asp.net/learn/ajax-videos/video-90.aspx
Thanks.