Quicktime reg key doesn't work on ONE machine

So I have been using QT7 Pro for a long time. I have it installed on three machines, and it works great on them. On a fourth machine, I needed to clean the disk and reload the OS (10.6.8), and set everything back up. One thing that needed to get reset was the QT7 Pro key. I enter it (and my "Registered To:" name) EXACTLY as displayed in my other operating QT7 Pro machines (including one also running 10.6.8), under Registration, and I get "Invalid Registration". Duh, what? My other machines are quite happy with it.

I tried rebooting, reloading QT7 from the Install disk. Nothing works. I keep getting "Invalid Registration".

Now, to the extent I have the wrong key (hard to believe, because this key is working dandy on three other machines!), I can't get it from Apple, since it was bought several years ago.