My computer died and I have the redemption code but it's already in use on the old computer. I need somehow change my CC to the new computer. Right now it's asking for a serial number but I am already a member...

I need to somehow transfer my CC over to a new computer.  Right now it says the redemption code has already been activated and yes that is for the old computer.  I bought a new one and I need it to be moved over to this one.  How can I do this?