<html>
<head>
</head>
<body>
<div id="div_1" name="div_1">Заполните форму</div>
<form>
<input type="text" id="input_1" name="input_1" maxlength="10" value="" oninput="validate();" onchange="validate();" onkeyup="validate();"><br>
<input type="text" id="input_2" name="input_2" maxlength="10" value="" oninput="validate();" onchange="validate();" onkeyup="validate();"><br>
</form>
<input type="button" id="button_1" name="button_1" value="Click" onclick="alert('ok!')" style="display: none;"><br>
<script>
function validate(){
var style = document.getElementById('button_1').style;
if (document.getElementById('input_1').value == ""){
style.display='none';
return;
}
if (document.getElementById('input_2').value == ""){
style.display='none';
return;
}
style.display='inline';
}
</script>
</body>
</html>