[critique] Cover of ~ half of "My Wild Love"

Singing is one of those things that I've always wanted but was always out of my reach; I have absolutely zero training, and my voice has a truly irritating quality to it. Every couple years, I figure, "Hey, this year I'll learn how to sing!"...but it never works.

Anyway, I'm now at that optimistic stage once again, so I figured I'd come here to look for advice. I chose "My Wild Love" by The Doors because, though the melody isn't that strong, it's simple and Jim Morrison had a very narrow vocal range (like me, alas...). I know this cover sounds horrible; in fact, I stopped midway through the song just because hearing myself sing was too painful. I just want to know what I can do mechanically to improve, because I know absolutely NOTHING about singing mechanics.

Anyway, here's the URL:

http://soundcloud.com/dumbness/mywildlove