If you keep an array of field names of all of the checkboxes in the form, you can use [man]array_diff/man to figure out which fields weren't POST'ed. Simple example:
$fields = array("checkbox1", "checkbox2", "checkbox3", "checkbox4");
// simulate POST'ed data
$_POST = array('checkbox1' => 'foo', 'username' => 'brad', 'checkbox4' => 'bar');
$missing_fields = array_diff($fields, array_keys($_POST));
print_r($missing_fields);
output of the above code:
Array
(
[1] => checkbox2
[2] => checkbox3
)