PHP, get the button by name which includes script

You have to rethink the script:

• on line 3 you completely empty the $_SESSION[cart] on every page load!
• you use a deprecated function: mysql
• you use unnecessary 'form' tags
• you check for $_GET input only on the last product, in a bad way

Here is a start:

<?php
session_start();
// initialize session var only ONE TIME
if (!isset($_SESSION["cart"])) {
    $_SESSION["cart"]= array();
}
// store a new element ID
$elId="";
// check $_GET input and validate it
if(isset($_GET["elId"])){
    // !! filter $_GET data somehow (e.g. make sure it is_numeric)
    $elId=preg_replace("/[^0-9]/","",$_GET["elId"]);
    // you could check in DB if the $elId is a valid value
}
// update SESSION if elId is not empty after validating $_GET
if (!empty($elId)) {
    // if not already in array, initialize field
    /* 
    use a multidimensional array to count how many products 
    of one type are in the cart, eg: $_SESSION[cart][343]=3; 
    aka Three products with id: 343
    */
    if (!isset($_SESSION["cart"][$elId])) {
        $_SESSION["cart"][$elId]=0;
    }
    // update cart
    $_SESSION["cart"][$elId]++;
    // ! user should be alerted, e.g:
    echo "<p>New product added to cart!</p>";
}
// DB access
//include_once 'dbconnect.php';
require "dbconnect.php";
$sql="SELECT * FROM products ORDER BY name ASC";
// fetch results
// $query=mysql_query($sql);
/* !! USE mysqli INSTEAD !! in file dbconnect.php */
$conn = dbconnect();
$results = $conn->query($sql);
// start products' HTML
echo "<a href='cart-display.php'>Go To Cart</a>";
echo "<table>";
// again, use mysqli
// while($row=mysql_fetch_array($query)){
while($row = $results->fetch_array()) {
    // * <form> tags are unnecessary, <a> tags are sufficient
    $elId=$row["id_product"];
    echo "
        <tr>
        <td>$row[name]</td>
        <td>$row[description]</td>
        <td>$row[price]</td>
        <td>$row[id_product]</td>
        <td><a href='?elId=$elId'>Add to cart</a></td>
        </tr>
    ";
}
echo "</table>";

?>

And the dbconnect.php:

<?php
function dbconnect() {
    static $conn;
    if (!isset($conn)) {
        $conn = mysqli_connect('localhost','username','password','dbname');
    }
    if ($conn === false) {
        return mysqli_connect_error(); 
    }
    return $conn;
}
?>