I downloaded the example and uploaded in my localhost.
My localhost is up and running with other examples in this book
I adjusted the parameters to connect to the database and created the table

$sDBServer = "localhost";
$sDBName = "test";
$sDBUsername = "root";
$sDBPassword = "admin";

The select

SELECT *
FROM `statesandprovinces`
WHERE name LIKE 'm%'
ORDER BY name
LIMIT 0 , 5

return:

Maine
Manitoba
Maryland
Massachusetts
Michigan

Well ... but when I run http://localhost/prove.it/AutoSuggestExample.htm and began to write in the box, State / Province, nothing happens!

It acts like a normal text box...

There is other evidence on this issue? Thanks to all