I want to display an image under the mouse (a finger to simulate a touch screen) when a mousedown event occurs and hide it when the mouseup event occurs, but when I do this,
This is untested - but is based on a working script of mine, so should be along the right lines. Basically, you have to make the layer that is in the way disappear for a moment, so you can use the elementFromPoint method and then make it come back.
$('.selector').click(function(e){
evt = e || window.event;
// make finger disappear
$('.finger').css({display:'none'});
// get element at point of click
starter = document.elementFromPoint(evt.clientX, evt.clientY);
// send click to element at finger point
$(starter).click();
// bring back the finger
$('.finger').css({display:''});
});