Reposting in forum PHP tags, so the color code shows:
$sql = "SELECT drinkid, title, date, rating FROM drinks WHERE title LIKE '".$_REQUEST['letter']."%' AND status = 'L'";
$sql = "SELECT drinkid, title, date, rating FROM drinks WHERE categoryid = '".$_REQUEST['catid']."' AND status = 'L'";
In both cases, you need the quotes around your comparisons... Also, in the first one, you need the % outside of the index... See if these work better for you.
Also, it is easier (but not required) if you capitalize the entire word for the specific MySQL words such as SELECT, FROM, WHERE, LIKE, UPDATE, DELETE, LIMIT, AND, OR, etc... (Makes it easier to pick out problems with the variables and the MySQL statements themselves.