Lauper's "Time After Time" made number one on the U.S. Billboard Hot 100 chart on June 9, 1984[SUP][/SUP] and remained there for two weeks. The song is currently considered Adult AC genre although I have heard it on Classic Hits as well.
Right. That was probably her first AC chart record ("She Bop" certainly wasn't), but there's an outside chance "Girls Just Want To Have Fun" might have been.
Unfortunately, the entire run of back issues of Billboard on Google Books from that record's chart life are missing and her singles discography omits the AC chart, so we don't know for sure.