I bought the Home & Student edition and installed it with no problem on a Quicksilver G4, an iBook G4 and a new MacBook. The first two were running 10.4.11 and the MacBook 10.5.2. This used up the three installs allowed.
Two weeks later the Quicksilver started playing up so i replaced it with the Mac Mini running 10.5.2, using the same security code and it's fine. I even had the Quicksilver and the Mac Mini running on the network together with the "same" MSO2008 at the same time for a couple of days before I retired the Quicksilver. So it shouldn't be a licencing conflict in your case either.
Since install I've installed the upgrade patch on all three and everything still works.
I wonder if you search for any old preference files that MS has left behind, you may find one that the new installer doesn't remove.