Activation problem

I have windows 7 that failed activation. Here is the situation. Way back when it first came out I purchased
the family 3 pack of Windows 7 Home Premium. I have it on 2 computers and had it on a 3rd but no longer. I made the mistake of thinking (like most normal people would) that I could have it on 3 computers at any given time as long as I
didn't try to put it on more than 3 at any time I was good to reinstall it since I had it on only 2 computers.
As I'm sure many of you know (I did not) that you only can install it once so the 3rd computer will not activate
as it's already been installed.

The problem is how can I get this activated without doing a complete install. I have purchased Windows 7 Home
Premium system builders (coming in the mail). Does anyone know if I can use the key from that to activate
Win 7 Home that is installed without have to do a complete install again.:eek:

Thanks