Occam's razor might suggest an answer like this:
$(document).ready(function(){
var pbClicked = false;
$("input[type=radio]").click(function(){
if (!pbClicked){
$(".pbNext").click();
pbClicked = true;
}
});
});
DEMO:
$(document).ready(function(){
var pbClicked = false;
$("input[type=radio]").click(function(){
var msg = (pbClicked) ? 'ignored' : 'clicked';
if (!pbClicked){
$(".pbNext").click();
pbClicked = true;
}
$('#msg').html(msg);
});
$('.pbNext').click(function(){
$(this).css('background','blue');
});
});
#msg{position:fixed;right:15px;font-size:1.3rem;text-align:center;}
.pbNext{width:100px;height:40px;background:pink;}
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.2.4/jquery.min.js"></script>
<div id="msg"></div>
<input type="radio" />
<input type="radio" />
<input type="radio" />
<input type="radio" />
<div class="pbNext"></div>
If you have multiple buttons to track, and you want the user only to be able to click each button once, then you can use an array to keep track of the buttons that were clicked. It will be easiest if you add an ID to each element to be tracked. Here is an example (Note that the 3rd checkbox has been specifically permitted to toggle, whereas the other 3 are restricted by their presence in the array of clicked checkboxes.):
var tmp_id, arrClicked = []; //vars created outside fns that use them
$("input[type=checkbox]").click(function(){
tmp_id = this.id.split('_')[1];
if (arrClicked.indexOf(tmp_id) == -1){
$(".pbNext").click();
arrClicked.push(tmp_id);
}
else if(tmp_id == 3){ $('.pbNext').click(); } //Allow id 3 to be re-clicked, just to show
$('#msg').html(JSON.stringify(arrClicked));
});
$('.pbNext').click(function(){
$('#cb_'+tmp_id).parent().toggleClass('a'+tmp_id);
});
#msg{position:fixed;right:15px;font-size:1.3rem;text-align:center;}
button{margin-top:15px;}
div{width:150px;padding:15px;border:1px solid #ccc;}
.a1{background:palegreen;}
.a2{background:lightpink;}
.a3{background:lightblue;}
.a4{background:palegoldenrod;}
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.2.4/jquery.min.js"></script>
<aside id="msg"></aside>
<div><input type="checkbox" id="cb_1" /></div>
<div><input type="checkbox" id="cb_2" /></div>
<div><input type="checkbox" id="cb_3"/></div>
<div><input type="checkbox" id="cb_4" /></div>
<button class="pbNext">Does Nothing button</button>
jsFiddle version that you can play with