If you're looking for users who have a price of $20, and you input 20, your SQL would look like:
SELECT *
FROM customers
WHERE price_min < '20'
AND price_max > '20'
Notice something wrong? I think you should be doing:
$query = "SELECT *
FROM `customers`
WHERE `price_min` <= '" . $_POST['price'] . "'
AND `price_max` >= '" . $_POST['price'] . "'";
Notice how 20 is now included in the result? So if someone has 20 as their min price, and 50 as their max, it should bring a result back.
As for not returning any results, are you 100% sure there are people listed at that price range you specify?