No, he shouldn't have to. Generally in these situations, if he were to call Microsoft and tell them that he needs to replace the motherboard and needs his OEM (Original Equipment Manufacturer) version of Windows unlocked, they would do it. Leo says Microsoft's "genuine advantage" has so many false positives (meaning that Windows tells the user their copy is pirated even though it isn't), that Microsoft deals with this on a regular basis.
John was concerned about the EULA (End User License Agreement) because he actually built his own PC and got an OEM version of Windows. Leo says a lot of companies will sell an OEM version of Windows if you buy a motherboard from them. So technically, since John bought the parts, that makes him an OEM. Leo also thinks the biggest concern from their point of view is that they don't have to support the OEM versions. When you get an OEM version of Windows, you're supposed to go to the OEM.