Well, I've only got a few pounds of other software... but this IS a common protection scheme
It has also been incredibly common, in the Windows world, to have to perform full uninstalls
followed by comprehensive registry sweeps, to clear up after a bad software installation.
Not every piece of software will tolerate simply being re-installed over a previous installation.

Don't take the piracy bit personally, if you're not guilty. I'm not accusing you.
There are just very few things, in my experience, which can cause your issues.
I probably was, however, a bit closed-minded in saying, "the ONLY other possibility", because
I'm sure I missed a couple other extremely remote ones... so I'll buy that.

Still:
A serial is stored on your hard drive somewhere... either in a registry key, or in a config file, or less
commonly, encrypted into the actual game binary (or some companion executable) at install time.
Some software checks for valid licensing on every load, while some will only check periodically.
In either case, things better hash out, or the piece of software will not operate properly.

Very common for software that is at high risk of being pirated. (or that the authors perceive as high risk)
Heck, if you think $260 gives you the right to easy living, with regard to copyright protection... try telling
it to someone paying $5000 ~ $8000 for the latest whizz-bang CAD software... complete with hardware
dongle that, if tampered or damaged, prevents the software from operating until they get a new one

If you don't feel like uninstalling and/or cleaning up your registry, try calling tech support... I hear
they're very good, and will likely get you going quicker than posting here and waiting for answers.

Hope you get it up and running again soon.