One thing to remember here is that CDs were not very common yet, and this 17-year-old boy was probably listening to either vinyl records or cassettes, both of which make it difficult to listen to a single track! So rather than a single song, I'd go for a full album or at least half of one. Taking a look at the top albums of 1984 (to account for access lag) and 1985, you've got your pick of the following (among many others):
Purple Rain, Prince
The Smiths, The Smiths
Born in the USA, Bruce Springsteen
Songs from the Big Chair, Tears for Fears