What song was it in the movie p.s I love you; it was also in Gilmore Girls.?

In the movie p.s I love you, after Jerry dies, she's watching a movie and in the movie the song plays. Also, In Gilmore girls they are watching the movie with the same song. Lyrics are like "The lights have lost their glimmer, and all because of the man that ran away." Also, her voice was like old school. Any idea?