Last year I encountered the same problem with the hard disc. I just contacted SDL Support and explained the situation, and they renewed my SDL Trados Studio licence without problems.
Paula Zucherelli wrote:
I have a Studio 2011 Freelance Plus license. I had it activated on two computers. One hard disk failed and had to be replaced before I had the chance to return the license. I have absolutely no idea how to reactivate it or recover it for the new hard disk. Any ideas will be more than welcome.