I'm looking at 1984 and a little earlier to make sure it doesn't go past 1985. Also because as a (USA, 1990s) teenager, my ability to acquire music was mostly taping off the radio and getting albums used, so if I was feeling like hearing a specific song, either I would have had to have the presence of mind to tape it or I would already have to have the album. Either way that implies some kind of foresight and access, unless the dumping was far enough in the past that he could have gone to a music store or taped off the radio about it.

Total Eclipse of the Heart might be too torchy for some guys, but it's super satisfying to sing along with.

Love Stinks is nicely shouty.

Tainted Love is a little more appropriate for someone who is doing the dumping, but came out comfortably in 1981.