I have to start this off with the legality: I am strongly under the impression that Microsoft does not want you to transfer your MS Office from one computer to another. They want you to purchase a new copy and you agreed to do this when you accepted the license upon opening/installing the program.
However, if you DO NOT have your key the only way you could find it would be in the registry. You may want to look at this site for more info:
(WS) Building off of the previous statements, Microsoft does sell single system licenses. That is to say that one disc means one computer. If by transfer you mean copy over program files, the Microsoft suite will, most assuredly, not work. If you uninstalled the Microsoft software on the old system, which happens to dissociate the key with the computer, you may be able to re-install it on the newer system. This, along with what was mentioned above, is, of course, your decision and you should use notable discretion in making it.
Copying the installed Microsoft Office 2003 to another drive won’t really work at all. This is because you need the original installer package for you to use your MS Office to another drive or computer unit.