I entered my SP3's default product key, and that worked, but after that, Windows Setup says "Something Happened: Setup failed to determine supported install choices." What does that mean, and how do I solve this problem? There weren't any alternate options for me to choose; everything I selected was the only option available.
I've never owned or heard of a computing device where MS' standard installation media didn't work. That being said, MS does have a site specifically for SP3 support, where it's possible to download recovery media specifically for the SP3. That's probably what I'd try:
Download a recovery image for Microsoft Surface
If that doesn't work I'd try the SP3 forums on this site and MS support.