You may want to add an Or die statement, this will help in weeding out errors:
(also try using apostrophes around your '$values' )
Change:
$sql = "INSERT INTO customer (first, last, phone, dlnum, state, email)" .
"VALUES ($first, $last, $phone, $dlnum, $state, $email)";
To this:
(sql statement should be all on one line)
$sql = "INSERT INTO customer (first, last, phone, dlnum, state, email)
VALUES ('$first','$last','$phone','$dlnum','$state','$email')";
$result = mysql_query($sql)
or die("ERROR: Values not entered into Table");