I need to install Microsoft Office 2003 for some reasons related to compatibility with Luddites.
I can buy an Office 2007 "open license" at the university where I am a faculty member, and I have seen the Microsoft downgrade chart which states that I have downgrade rights.
I can find Office 2003 media.
But how do I get a legitimate license key or activation code for this downgraded version of Office?
You will have to ask your university support. Whoever administers the licenses will have to log into the Microsoft eOpen site. It's listed there.
Microsoft Licensing is only going to give that code to someone who's got the Agreement number and License number (not license key). Which brings us back to Joseph's answer - you're only going to be able to get it through University IT.
However, if you put in a helpdesk ticket that makes it as easy as humanly possible, it should improve your odds. The US number is 888-352-7140, per MS Licensing.
I recommend you ask your University technical support, software licensing department, or the University bookstore (if that's how you're buying it).
Our university switched from Open to Select several years ago. At least back in those days, we found the "Open" media did not work with "Select" keys and vice versa. So when you say "I can find Office 2003 media." that media may not work with the license key you get from one of those University sources I mentioned.
The same people who can provide you a key can also provide you with matching media.
This site may contain the answers you are looking for:
Resources to help you activate a license in Microsoft Office programs
and in particular: About product activation in Microsoft Office System products
Assuming this is a legitimate copy of Office and you are permitted to install the older version under the license terms you purchased it under, then contacting Microsoft directly may be the best course.