I have been successfully naming many songs lately, where i didn't know the artist and title but knew some of the lyrics.
You need to begin with a browse of the various song lyric websites, for example -
www.lyrics.com, www.azlyrics.com (11more lyrics sites down their left hand column), www.lyricsmode.com, www.elyrics.net, www.get-lyric.net, www.seeklyrics.com and
www.songmeanings.net.
These sites all enable one to search based upon the known lyrics, which one types into the text box at the top. A search yields hundreds of results, bit like any search engine.
I have been using wikipedia.org for more info on the various released numbers and albums by a given artist, and it works nicely in conjunction with Youtube once the lyrics sites provide you with various leads.
This way you can be in control of your song hunting ! It is fun !