I had something like this on the Wii, it was an American Idol game, and I didn't know most of the songs. I think Rock Band also let you sing, I had the Beatles one, which I did a lot better at!How about a Karaoke game? Not one of those silly things where you're pushing buttons while some music plays, one where you get your microphone out and you SING!
I don't know why the PC hasn't done it, though. Not enough demand? *shrug*