First of all, you're doing it wrong when building the query.
Doctrine escape parameter that you give to the query, so you don't have to use mysql_real_escape_string
on your own.
$str = "Developer in the hell";
$srchKey = "%" . $str . "%";
$q = Doctrine_Query::create()
->from("Movie as m")
->where('m.name LIKE ? or m.keywords LIKE ?', array($srchKey, $srchKey))
->fetchArray();
About your search engine, you should have a look at the Searchable behavior. It will be more powerfull than a simple LIKE
query. But I don't know if it handle multiple term search like you want.
Or you can give a try to Lucene. A tutorial is available as part of the Jobeet tutorials.