When you change the motherboard, Windows considers it a completely new computer. The product key you have is currently "locked" to the Hardware ID of the old motherboard.
Since you don't have a support contract to talk to a human, you must use the Automated Systems to force the transfer. Here is the hierarchy of fixes, and you can try them in order (from easiest)
Method 1: The "Digital License" Transfer (Try this first)
If you had logged into a Microsoft Account on the old motherboard, your key might have been converted to a Digital License.
Go to Settings > System > Activation (or Update & Security > Activation on Win 10).
You will see an error (likely 0xC004F211). Click Troubleshoot.
Select the option: "I changed hardware on this device recently."
If it asks you to sign in, use your Microsoft Account.
Select your "old" computer name from the list and click Activate.
Method 2: The "Phone Activation" Bypass (The Robot)
If the troubleshooter fails, you need to use the automated phone system. This system does not require a support plan; it is a free automated robot. Note: The visual menu (slui 4) often doesn't appear in newer Windows versions, so we will do it manually.
Disconnect from the Internet. (This prevents Windows from instantly rejecting the key online).
Open Command Prompt as Administrator.
Type the following command to install your key again:
slmgr /ipk XXXXX-XXXXX-XXXXX-XXXXX-XXXXX
(Replace X with your actual 25-digit key).
Now, type this command to generate your Installation ID:
slmgr /dti
A box will pop up with a huge string of numbers. Write this down.
Call the Microsoft Activation Center for your country (Google "Microsoft Activation Center Phone Number [Your Country]").
Do not try to speak to a human. When the robot asks, say you are activating Windows.
Enter the Installation ID you got from step 4.
If the robot asks: "on how many computers is this software installed?" answer "Zero" or "One". (This is the critical question).
The robot will give you a Confirmation ID.
Back in your Command Prompt, type:
slmgr /atp <ConfirmationID>
(No spaces in the ID).
Restart your computer and reconnect the internet.
If the robot says "We cannot activate this product," you need to verify if your key is OEM or Retail.
Retail: Transferable. The methods above should work.
OEM (Original Equipment Manufacturer): These keys are cheaper "Business" keys often sold by third parties or pre-installed by Dell/HP. They die with the motherboard. Legally and technically, they can't be transferred. If you have an OEM key, you will have to buy a new one.
I hope you've found something useful here. If it helps you get more insight into the issue, it's appreciated to ACCEPT ANSWER. Should you have more questions, feel free to leave a message. Have a nice day!
VPHAN"