$(document).ready(function(){
$("#ab1").click(function (){
                    var otw = document.getElementById("badania");
                    var rbad = document.getElementById('aab1');
                    rbad.parentNode.removeChild(rbad);
                });
});

[HTML] pobierz, plaintext 
<div class="dane">RODZAJ BADA?:</div>
        <div id="badania"><div class="otwBadania">Badania</div>
        <input id="aab1" name="aab1" size="45"/>
        <img id="ab1"  src="./zamk.gif" />
</div>
[HTML] pobierz, plaintext 

$('#aab1').remove();