Since the thread was bumped anyway, and I’ve been on a '90s rock kick, I figured I’d nominate Matthew Sweet’s ‘Girlfriend’ as a candidate for having a decent if short fade-in to a (IMO) pretty rocking song (the song does fail the best fade-out test, what with not having any)
Cool video as well, among the earliest to incorporate anime (but not the first). VEVO video, so sorry for the ads.