<script>
    function verif(nameForm , radio){
        lesChoix = document.getElementById(nameForm).elements[radio];
        check = false;
        for (var i=0; i<lesChoix.length;i++) {
         if (lesChoix[i].checked) {
           check = true;
         }
        }
        return check;
    }
    function change(nameForm , radio,submit){
        if(verif(nameForm , radio)){
            document.getElementById(submit).disabled = false;
        }else{
            document.getElementById(submit).disabled = true;
        }
    }
</script>

<h1>Formulaire 1</h1>
<form id="1">
    <input onchange="change('1','gender','submit1')" type="radio" name="gender" value="male" > Male<br>
    <input onchange="change('1','gender','submit1')" type="radio" name="gender" value="female"> Female<br>
    <input onchange="change('1','gender','submit1')" type="radio" name="gender" value="other"> Other<br>
    <input id="submit1" type='submit' disabled />
</form>
<h1>Formulaire 2</h1>
<form id="2">
    <input onchange="change('2','gender','submit2')" type="radio" name="gender" value="male" > Male<br>
    <input onchange="change('2','gender','submit2')" type="radio" name="gender" value="female"> Female<br>
    <input id="submit2" type='submit' disabled />
</form>
<h1>Formulaire 3</h1>
<form id="3">
    <input onchange="change('3','gender','submit3')" type="radio" name="gender" value="male" > Male<br>
    <input onchange="change('3','gender','submit3')" type="radio" name="gender" value="female"> Female<br>
    <input  id="submit3" type='submit' disabled/>
</form>
<h1>Formulaire 4</h1>
<form id="4">
    <input onchange="change('4','gender','submit4')" type="radio" name="gender" value="male"> Male<br>
    <input onchange="change('4','gender','submit4')" type="radio" name="gender" value="female"> Female<br>
    <input onchange="change('4','gender','submit4')" type="radio" name="gender" value="other"> Other<br>
    <input  id="submit4" type='submit' disabled/>
</form>