Ooh - I love trivia questions like this! Alas, I don't know this one -- although I think Scandal had two #41 hits preceding "The Warrior" ("Goodbye to You," and I forget the other one). Gotta be something that was re-released, which would make me think "I Melt With You," except Modern English didn't have any other hits. ZZ Top had "La Grange" spend 3 weeks at #41, but their top 10s came later, I'm sure. Got any other hints?
Actually part of my hint will be to clean up a slight innacuracy. Let me rephrase:
What band of this era, which had two of their four Top 10 entries (and another two of their total 13 Top 40 hits) in 1984, also managed to have a song peak at #41 not once, not twice, but THREE TIMES?
I have an additional hint if that doesn't do it.
p.s. the La's peaked at #49 according to Allmusic. Correct on the Scandal, though.