checking at least one radio button is selected from each group (with jquery)

In the absence of any relationship between elements, or how to find the group names, I can only give you a pointer, but this should work (the check's triggered by clicking on the element of id="nextButton", but obviously this can be customised to any other appropriate event, such as $('form').submit(), for example):

$(document).ready(
function(){
  $('#nextButton').click(
    function(){

    var radioName = something; // use this if there's a relationship between the element
                               // triggering this check and the radio buttons

      if ($('input[name='+ radioName +']:checked').length) {
           // at least one of the radio buttons was checked
           return true; // allow whatever action would normally happen to continue
      }
      else {
           // no radio button was checked
           return false; // stop whatever action would normally happen
      }
    }
  );
}
);

$("input[@name='the_name']:checked").length;