In the sentence "The song "Singing in the rain" comes from the movie of the same name starring Gene Kelly, Debbie Reynolds, and Donald O'Connor", the word that is not capitalized that should be is the word 'rain' in the title of the song. The sentence should look like this:
"The song "Singing in the Rain" comes from the movie of the same name starring Gene Kelly, Debbie Reynolds, and Donald O'Connor"
Hope that helped =)