Aftur Heim (Back Home), the song written by Sigurjon (Sjonni) Brink and his wife Þórunn Erna Clausen, won the Icelandic national final.
here at RÚV's Eurovision pages.
Another song, You Knocked Upon My Door was in the semi final of 2010.
You can listen to the 15 songs here.
also see Iceland in 2010 (Hera Björk) and 2009 (Yohanna)