Thats wrong
Your log clearly shows Couatl has got an "Machine Mismatch" 25007 message from Esellerate, which means the product is in Trial now, but as I've said in my previous message, it's possible that if Couatl.exe is not running under Admin privileges or with some kind of Compatibility mode enabled, so it's the same AS IF the hardware was changed, because Esellerate it cannot access the registry keys because of permission issues.
Here we are again with pics
There wasn't obviously any need to send pictures, if I needed pictures, I'd ask for them. I never said I don't "believe" you have the Addon Manager stating the product is Active. That's precisely why I've said there must be a problem with Couatl permissions or compatibility mode.
The Addon Manager is not getting confused by Esellerate, and is reporting it as Active, because it runs under FSX so, if FSX itself is not having a problem with permission, the Addon Manager will inherit its registry access permissions and is reporting it as being Active, but if you have a problem with Couatl configuration and, for some reason, it can't access the registry ( well, it's Couatl is not even TRYING to access the registry directly, it's all done by Esellerate ), it won't be able to confirm the activation. Since GSX runs entirely under Couatl so, fact the Addon Manager thinks it's Active, doesn't have any meaning for it.
Could be you have another Esellerateengine.dll somewhere in your system ? Try to look in the following folders:
1) the FSX root folder
2) the C:\Windows folder
3) the C:\ProgramData\Esellerate folder
Only ONE copy must be present, the one under C:\ProgramData\Esellerate folder, if you have another copy in another place, remove it. It has been put there by other add-ons using ( outdated ) versions of Esellerate.
Don't waste your time reinstalling GSX, the problem is NOT GSX. Nothing related to the Activation is ever affected by installing/reinstalling, the installer doesn't do anything related to the activation, the issue is your system is not allowing Couatl (or, better, the Esellerate .DLL ) to access your activation keys in the registry.
Do you start FSX from another program ? If yes, don't.