Problem solved.
Heard back from Steinberg support by email today just now - they sent me a 32 digit code, which I put into my soft e-Licenser. Now I open up Cubase AI 7 and it says nothing about a time-limited application. So, I think that means I’m in!
Kudos to Steinberg support (“Chris Dobbs”), they got back to me within 1 working day with a complete fix for the problem.
Thanks for everybody’s help. I have no idea why it didn’t work, but now it does, so I am happy!