You are right, and saved my day! Thanks a lot!
It was messed up so badly that it would not even boot in safe mode. I needed to do a fresh installation of the originally shipped OS (Windows 8.1). When I tried to activate it, it grabbed it automatically from the BIOS. After this, I contacted Microsoft Help Desk. They told me to upgrade to Windows 10, and told me that if required, they would help regarding a free activation. I upgraded and voila, it was already activated.
Thanks again!