There were a couple of mentions of Don’t You (Forget About Me) upthread, but I strongly feel that this is the song that defines 80s music for me. 
If you look hard enough you can find one or two other Seona Dancing tracks on YouTube with the same sort of sensibility. They are, in my humble opinion, straight fire. @ShadowFacts, I think Gervais had as good a sense of the 80s sound as anyone. Almost a shame that band didn’t make it, but then we might not have had his career as a comedian to enjoy.
While Prince, Michael Jackson, and Madonna don’t have careers that were completely defined by the 80s, their greatest successes were in the 80s and their contributions shaped the musical landscape in profound ways. I would argue that the Thriller album basically rescued the entire music industry after years of stagnation; Prince was all over the charts throughout the 80s, either as an artist (24 songs charted on Billboard’s Hot 100) or as a writer producer (for artists like Sheena Easton, Sheila E, Chaka Khan, Cyndi Lauper, Stevie Nicks, Sinead O’Connor, The Time, The Bangles, Vanity 6, Tom Jones (he covered Kiss with Art of Noise), Patti LaBelle, Tevin Campbell, and more); Madonna’s Like a Virgin album was revolutionary and she then made a career out of pushing the boundaries for the rest of the decade. I don’t think you can dismiss any of those three for their influence on the sound of the 80s—they were everywhere, with people just trying to keep up.