Same issue here, except I didn't change hardware or reinstall. The only thing that changed was my laptop was upgraded to Sierra, which I'm guessing somehow counts as a "new license" (even though it is the same machine).
I have both a Mac Pro desktop and Macbook Pro laptop. I've had Parallels desktop 9, 10 and 11 installed on both for as long as I can remember (though not at the same time, obviously). I very rarely use PD on my laptop, but I install it as a convenience on the off chance that I might need access to Windows while traveling. If I had to guess, I'd say I've launchd PD on my laptop maybe twice in the past year or two.
Today I launched PD on my Mac Pro and was greeted by the "Active Parallels Desktop" window. I entered my paid/valid license key, was informed "This license is already in use. ...", clicked "Activate on This Mac" only to end up with the "Unable to confirm the produce license" prompt. So, add me to the queue of people that require a support representative to fix the issue so they can get back to work.
For what it's worth, I did not know about the "1 purchase = 1 license = 1 machine" EULA nor had I ever experienced issues in the past. I knew one purchase did not equal *limitless* installations, but most software vendors today accept that one person may use multiple devices so they allow for multiple installations (e.g. Microsoft Office allows for 2 installations: 1 desktop, 1 laptop). Parallels licensing terms seems rather draconian to me, but that's their choice. Next time I'm debating between paying to upgrade Parallels Desktop vs. switching to VMWare Fusion (better licensing terms) or VirtualBox (free), I'll take this into consideration.
