Your replacement variables will get escaped and quoted automatically by PDO, which means you cannot have a variable within quotes.
change the following:
$statement = $db->prepare("SELECT * FROM news WHERE headline LIKE :title
OR content LIKE :content
OR author LIKE :author
ORDER BY id DESC");
$statement->execute(array('title' =>'%'.$query.'%',
'content' =>'%'.$query.'%',
'author'=>'%'.$query.'%'));