It's got something to do with GPO, I'm not doing that side of things, so will have to sit with the network guys and figure out what in the Policies is preventing the Admins from installing correctly.
We took a brand newly built laptop, Ghosted the OS, logged on as LOCAL Admin and did the install, that worked ok, and put Office in the "All Users" profile. Then Office was available to anyone who logged in after that.
If we logged into the network first, and then tried doing the install, it didn't work correctly (although there is no errors or indications that there is a problem). So it's gotta be something that the GPO is blocking.
Oh, it's Office 2003 Pro.