'Serial Key in use' when reinstalling CnC3 Kane's Wrath

Having removed my CnC3 game a couple of months/years/whatever ago, I have just tried to reinstall it and it says that the serial number I'm entering has already been used - well of course it has - BY ME.  I happily accept that because I have registered my game once before it will show up as a 'repeated' serial number, but what is not helpful is the lack of topics on this.  Why is it that Google throws up more pages about illegally obtaining serial keys than it does help pages about this from EA?  It's like EA doesn't give a hoot.  It shouldn't be THIS difficult to find a solution to a genuine and minor issue such as reinstalling one of their products.  I thought I'd enjoy a nice evening of playing CnC3 again for old time's sake, but here I am trawling forums and Googling solutions trying to find out legitimate ways of playing a game that I've already spent my hard-earned money on.

I'm dreading having to reinstall again in the next few months if/when I buy an SSD drive and have to start from square one.