Why my stop and play button wont "work" ?

var playlist = new Playlist();

var hereComesTheSun = new Song("Here comes the sun", "The Beatles" , "2:54");
var aintNoRest = new Song("Ain't no rest for the wicked", "Cage the elephant" , "3:54");
var fadeToBlack = new Song("Fade to black", "Metallica" , "5:54");


playlist.add(hereComesTheSun);
playlist.add(aintNoRest);
playlist.add(fadeToBlack);

var playListElement =   document.getElementById("playlist");

playlist.renderInElement(playListElement);
//////////////////////////////////////////

var playButton = document.getElementById("play");

playButton.onclick = function () {

  playlist.play();
  playlist.renderInElement(playListElement);

}
var stopButton = document.getElementById("stop");

playButton.onclick = function () {

  playlist.stop();
  playlist.renderInElement(playListElement);

}
var nextButton = document.getElementById("next");
nextButton.onclick = function () {

  playlist.next();
  playlist.renderInElement(playListElement);

}

function Song(title, artist, duration) {

    this.title = title;
    this.artist = artist;
    this.duration = duration;
    this.isPlaying = false;
}

Song.prototype.play = function() {
  this.isPlaying = true;
};

Song.prototype.stop = function() {
    this.isPlaying = false;

};

Song.prototype.toHTML = function() {


  var htmlString =   "<li";

 if (this.isPlaying) {
  htmlString += " class = 'current'";

 };
  htmlString += ">";
  htmlString += this.title;
  htmlString += "-";
  htmlString += this.artist;
  htmlString += "<span class='duration'>";
  htmlString += this.duration;
  htmlString += "</span></li>";

  return htmlString;
};

function Playlist() {

  this.songs = [];
  this.nowPlayingIndex = 0;
};

Playlist.prototype.add = function(song) {

  this.songs.push(song);
};

Playlist.prototype.play = function() {
var currentSong = this.songs[this.nowPlayingIndex];
  currentSong.play();
};

Playlist.prototype.stop = function(){
var currentSong = this.songs[this.nowPlayingIndex];
  currentSong.stop();

};

Playlist.prototype.next = function() {
  this.stop();
  this.nowPlayingIndex++;

  if (this.nowPlayingIndex === this.songs.length) {
  this.nowPlayingIndex = 0;

  }
  this.play();
};

Playlist.prototype.renderInElement = function(list) {

  list.innerHTML = "";

  for (var i = 0; i < this.songs.length ; i++) {

   list.innerHTML += this.songs[i].toHTML();   
  }

};