I have a carrier bag full of dead Nintendo power supplies for the NES/SNES (9V, 1.3A).
This would suggest to me that it's a pretty common part to fail. I suspect one or two might just have a blown fuse but the one I've taken apart appears to have a faulty transformer.
This must be a standard part but it doesn't have any meaningful markings so I don't really know where to start looking for a spare.
And would it be worth doing? I can't imagine a new transformer costs more than �2...