I am guessing it may have to do with the fact you are trying to run old software on a new operating system for which it was not designed.
8.1 was back in the days of Windows XP.
What is your OS?
Does Archicad run in demo mode or not at all?
If demo mode then there is a problem with your key.
If not at all it may be the OS.
Have you tried the license activation tool to see if the key is being recognised and the license is valid?
Can be found here ...
http://www.graphisoft.com/downloads/licensing/
Barry.
One of the forum moderators.
Versions 6.5 to 27
i7-10700 @ 2.9Ghz, 32GB ram, GeForce RTX 2060 (6GB), Windows 10
Lenovo Thinkpad - i7-1270P 2.20 GHz, 32GB RAM, Nvidia T550, Windows 11