Extreme, I believe, was the band behind "More Than Words", back in the halcyon days of glam rock.
Lou BEGA did "Mambo Number 5" which became a cross-media reference on PM Junior's Pugad Baboy.
Didn't Right Said Fred also make the hit "Don't Talk Just Kiss" or something to that effect?
Modern English also did "Ink And Paper" and "Hands Across The Sea", not the smash "Melt With You" was but still hits of their era.
Lady singer DJ Alvaro did "Tipo Kong Lalake".
At the risk of sounding like I am on an acid trip, how about the mythical band The Wonders and their hit "That Thing You Do" form the movie of the same title.
And Deep Blue Something's "Breakfast At Tiffany", and "Buttercup" by The Foundations.
Does "Big In Japan" by Alphaville count?
And who was that guy who did "Dying Inside", the black guy, oldish.
And "Fixing A Broken Heart" by a mid-1990's band whose name escapes me at the moment.