Q: Office for Mac Problems

I have Office for Mac 2004, which supposedly allows 3 installations, with 3 different Installation Key Numbers. I have installed it on 2 Macs, and all is fine until I try to use both computers at the same time. Then I get a message on the Mac on which I installed it second telling me that "a copy of this programme is already open", and if I want to continue I have to close down all the Office applications on the first machine! Very frustrating! I am almost certain I used a different installation Key for the two machines but cannot find the recoed of what Key number was used. If I look in "Properties" I see that the product ID numbers are the same until the last group of digits which are different on the two machines. How can I find which installation Key numbers I used on each machine, and is there any way I can get aouns this problem. I am nervous to unistall and reinstall in case I am then not allowed to reinstall with a previously used Key!?
Thanks,
Kendrew.