If you have already done that and are looking for another solution, unfortunately you have had bad luck.
Before you move to a new PC, you must log off or deactivate your Windows license from the old computer in order to make it available again.
By the way, it does not necessarily have to be that you are facing the problem if you have bought a new computer, but it can be enough if so-called system-relevant components are exchanged.
This is the same for Windows as if it were a completely new PC.
The system-relevant components include e.g. Mainboard, CPU, hard drive and in some cases, even the graphics card (albeit the exception) to be the trigger.