Well I ran the install file again that I had downloaded at the time and ran it as an administrator.
I then installed the software to e:\program files rather than c: and the install completed OK.
When I ran the software after that it was already licensed with the license it had had previously, and the software ran without the Register PhoenixDLL.dll error.
Interestingly enough, my machine is on a Windows domain and it seems to run without issue.