Disabled inputs do not trigger change and click events on FireFox.

$('li:eq(1)').click(function(e){
    if($.trim($('#input1').val()).length != 0){
        $('#input2').prop('disabled', false);
    }
});

http://jsfiddle.net/SVtDj/10/

instead of trim() you can use jQuery $.trim()function which is cross-browser:

$('#input1').change(function(){
    if($.trim($(this).val()).length != 0){
        $('#input2').prop('disabled', false);
    }
});

demo

Your code is fine. The issue is that .change() requires a lost of focus (blur) before it triggers. Try changing it to .keyup()

http://jsfiddle.net/SVtDj/6/

additional: this is probably the effect you were going for

$('#input1').keyup(function(){
     $('#input2').prop('disabled', $(this).val().trim().length == 0);
});​

To extend Ramison's answer

If you want to toggle the disability on #input2 you can simple:

$('#input1').change(function(){
    var isDisabled = !$.trim($(this).val()).length;
    $('#input2').prop('disabled', isDisabled );
});

And the demo: http://jsfiddle.net/SVtDj/7/

The issue is Firefox needs you type 'enter' or do something else so input1 looses the focus after having wrote in input1 to cast the "onchange" event I think. Maybe this question is linked to yours, and it made me try the following that works with Firefox. (I didn't try it on other browsers)

$('#input1').bind('input',function(){
  if($(this).val().trim().length != 0){
    $('#input2').removeAttr('disabled');
  }
});​

That's because in FF, when an input is disabled it is really disabled (it doesn't receive mouse clicks).

Clicking on your disabled element doen't produces a blur event (focus lost) on input1, so the onchange doesn't gets fired.

You can workaround this easily with some classes and jQuery. For example:

<input class=disabled id=input2>

some css:

.disabled { background: #888; }

and then...

$(function(){
  // disable keypresses on "disabled" input
  $('.disabled').keypress(function(e){
    e.preventDefault;
    e.stopPropagation;
    return false;
  });
  // doesn't allow to focus
  $('.disabled').focus(function(e){
    $(this).blur();
  });
});

to activate the "disabled" element:

$('#input2').removeClass('disabled');

Check it here: http://jsfiddle.net/SVtDj/11/

See the answer of @Andy E in this post Jquery event on a disabled input, i think it is the best solution to resolve your problem.