The literal date values need to be quoted: they are strings, not numbers. Also, you left out the "$" on the PHP variables names used in your original query. It should look something more like:
"SELECT c.Firstname, c.Lastname, v.Title from Customer as c
inner join Loan as l on (c.customerId = l.customerId)
inner join Video as v on (v.videoId = l.videoId)
where l.date >= '$sDate' and l.date <= '$eDate'"
For debugging purposes, you might want to do something like the following:
$sql = "SELECT c.Firstname, c.Lastname, v.Title from Customer as c
inner join Loan as l on (c.customerId = l.customerId)
inner join Video as v on (v.videoId = l.videoId)
where l.date >= '$sDate' and l.date <= '$eDate'";
$result = mysql_query($sql) or die("Query failed: [$sql]: " . mysql_error());
Eventually you'll want to get rid of the "or die()" and do some more robust error-handling that won't output database details to the user if it fails.