Eddy Grant is Romancing the Stone
Thanks to the tip from Nick regarding the musical history of why the soundtrack to Romancing the Stone was never released on CD.
Wikipedia has a brief mention of the soundtrack on the movie’s page. Eddy Grant wrote the title track for the movie, but only the guitar solo from the song was included in the movie. The rest of the music from the movie is provided by Alan Silvestri.
Here’s the video for Eddy Grant’s track: