<script>
    radios = ["part1","part2","part3","part4"];
    idForm = "monform";
    idBouton = "monbouton";

    function verif(radio){
        lesChoix = document.getElementById(idForm).elements[radio];
        check = false;
        for (var i=0; i<lesChoix.length;i++) {
         if (lesChoix[i].checked) {
           check = true;
         }
        }
        return check;
    }
    function change(){
        ok = true;
        for(var i = 0;i < radios.length ; i++){
            if(!verif(radios[i])){
                ok = false;
            }
        }

        if(ok){
            document.getElementById(idBouton).disabled = false;
        }else{
            document.getElementById(idBouton).disabled = true;
        }
    }
</script>

<h1>Partie 1</h1>
<form id="monform">
    <input onchange="change()" type="radio" name="part1" value="male" > Male<br>
    <input onchange="change()" type="radio" name="part1" value="female"> Female<br>
    <input onchange="change()" type="radio" name="part1" value="other"> Other<br>
<h1>Partie 2</h1>
    <input onchange="change()" type="radio" name="part2" value="male" > Male<br>
    <input onchange="change()" type="radio" name="part2" value="female"> Female<br>
<h1>Partie 3</h1>
    <input onchange="change()" type="radio" name="part3" value="male" > Male<br>
    <input onchange="change()" type="radio" name="part3" value="female"> Female<br>
<h1>Partie 4</h1>
    <input onchange="change()" type="radio" name="part4" value="male"> Male<br>
    <input onchange="change()" type="radio" name="part4" value="female"> Female<br>
    <input onchange="change()" type="radio" name="part4" value="other"> Other<br>
    <input  id="monbouton" type='submit' disabled/>
</form>