Update this line:
$UpdateQuery->bindColumn("FileName", "s", "".((isset($_FILES["fileField"]))?$_FILES["fileField"]["name"]:"") ."", "WA_DEFAULT");
to:
$UpdateQuery->bindColumn("FileName", "s", "".((isset($_FILES["fileField"]))?$_FILES["fileField"]["name"]:"") ."", "WA_IGNORE");
That will tell it to ignore blank values for that field.