"document.getElementByClass is not a function"

You probably meant document.getElementsByClassName() (and then grabbing the first item off the resulting node list):

var stopMusicExt = document.getElementsByClassName("stopButton")[0];

stopButton.onclick = function() {
    var ta = document.getElementsByClassName("stopButton")[0];
    document['player'].stopMusicExt(ta.value);
    ta.value = "";
};

You may still get the error

document.getElementsByClassName is not a function

in older browsers, though, in which case you can provide a fallback implementation if you need to support those older browsers.

Before jumping into any further error checking please first check whether its

document.getElementsByClassName() itself.

double check its getElements and not getElement