Template for submit via ajax to Guest Entries plugin
There are some problems with your JavaScript that I expect is the cause of your issue.

From your code I'm assuming you're using jQuery Validate to validate the form before submission. Your first issue is the line

event.preventDefault();


within the submitHandler() method – jQuery Validate will actually prevent the default form submission for you, so this line is redundant. Also, there is no variable called event, so that's going to cause trouble.

The second issue is that you're using the wrong syntax for the $.ajax() method. Considering your current code, I believe you want to use the $.post() method instead.

Finally, you're serializing the wrong object – $(this).serialize() should actually read $(form).serialize().

With the above issues fixed, your code should look like this:

$(document).ready(function () {

    $('form#brick').validate({

        ignore: ":hidden",

        rules: {
            "fields[firstName]": {
                required: true,
            },
            "fields[lastName]": {
                required: true
            },
            "fields[email]": {
                required: true,
                email: true
            }
        },

        messages: {
            "fields[email]": "Email is required"
        },

        submitHandler: function (form) {

            var data = $(form).serialize();

            $.post('/', data, function (response) {
                if (response &amp;&amp; response.success) {
                    $('#thanks').fadeIn();
                    $('#brick').fadeOut();
                } else {
                    alert('An error occurred. Please try again.');
                }
            });

        }

    });

});


Finally, for some pointers on how you could handle errors within the response payload, see this thread.