Here's the script, rewritten to use the suggestions above and a change to your no-cache method.
<?php
// Simpler way of making sure all no-cache headers get sent
// and understood by all browsers, including IE.
session_cache_limiter('nocache');
header('Expires: ' . gmdate('r', 0));
header('Content-type: application/json');
// set to return response=error
$arr = array ('response'=>'error','comment'=>'test comment here');
echo json_encode($arr);
?>
//the script above returns this:
{"response":"error","comment":"test comment here"}
<script type="text/javascript">
$.ajax({
type: "POST",
url: "process.php",
data: dataString,
dataType: "json",
success: function (data) {
if (data.response == 'captcha') {
alert('captcha');
} else if (data.response == 'success') {
alert('success');
} else {
alert('sorry there was an error');
}
}
}); // Semi-colons after all declarations, IE is picky on these things.
</script>
The main issue here was that you had a typo in the JSON you were returning ("resonse" instead of "response". This meant that you were looking for the wrong property in the JavaScript code. One way of catching these problems in the future is to console.log the value of data and make sure the property you are looking for is there.
Learning how to use the Chrome debugger tools (or similar tools in Firefox/Safari/Opera/etc.) will also be invaluable.