You could buy a nominally identical motherboard, from the same production run, and the MS activation servers wouldn't recognize the new board as the same.
Whether there's a way to hack the new board to make it a clone of the original, that's beyond my knowledge. It might be as easy as swapping the BIOS chips.
You changed the mobo, you have to call them I guess. Good luck trying to clone it! Crucial infos (related to activation and to prevent piracy) are written in the BIOS EEPROM by the manufacturer and there ain't there no more. The MAC address is among them and it's not the same. I won't discuss the original Hardware Hash not there any more.
Just for reference, I did an OEM win 7 upgrade to 10. Then my msi z77a-g46 mobo failed. RMA, installed, booted just fine.
And then THAT mobo failed, of course it can't be bought for a reasonable price anymore, so I get to be creative -- I hear that you can talk them into activating if it was to replace a broken mobo. They want everyone on Win 10 so bad.
As an aside, have also cloned my 10 install to a new ssd AND pulled 2 x2tb hdd for 1 4tb and windows never blinked.
Edit: also changed gpu AND replaced RAM, again no problem booting right up. In fact, the cpu is the ONLY original component from upgrade. (Ok, case, psu, and monitors too).
The activation agents are under no obligation to reactivate a repair-replacement mobo if the copy of Windows was a free upgrade and not an OEM or retail copy. You may get lucky but don't count on it. The problem is that the digital entitlement is not available in the new mobo's firmware and if there is no COA to fall back on then there is no way to verify entitlement for the upgrade.
Gabe Aul did say that the free copy of Windows 10 was only good for the life of the computer, and that means the specific mobo installed on unless the upgraded copy of Windows had a stand-alone license. If it did, then the free upgrade was transferrable with it. Otherwise it dies with the mobo.
The digital entitlement is saved on Microsoft activation servers via the internet along with a matching hardware ID that Windows generates from the hardware configuration. Every time Windows boots it reads the hardware configuration of the computer and generates the hardware ID. If the newly generated hardware ID matches the previous hardware ID stored in the registry, then it simply remains activated. If the newly generated hardware ID does not match what is stored in the registry, Windows will deactivate and then if connected to the internet send the new hardware ID to Microsoft activation servers. If a match is found, and the Windows version is the same then Windows will activate based upon that return from Microsoft activation servers.
My neighbor just had to replace his motherboard. He replaced it with a totally different model and brand because the broken one is no longer available. Windows loaded properly, without activation of course. He used the activation screen to open a chat with Microsoft. They first asked for his old activation key (a Windows 8 key) and his Microsoft account. They them took remote control of the PC and checked a number of things, including the full hardware configuration of the PC, presumably to see the motherboard information. They also asked to see proof of purchase of the new motherboard, so we opened up my neighbor's Amazon.com account and showed the invoice. Once that was done the agent ran a command prompt program of some sort, entered the old key, and Windows activated properly. It was easy and took about five minutes. The remote session was slick.