No è concettualmente sbagliato :
pagina1.php
codice:
<script language="javascript" type="text/javascript" src="C:/Bitnami/wampstack-5.4.30-0/scripts/JQuery/jquery-1.11.1.min.js">
 
function call_ajax(){
    $.ajax({
        type: "POST",
        url: "pagina2.php",
        dataType: "html",
        data: "matricola=" + $("#matricola").val() + "&stato=" + $("stato").val() + "&sn=" + $("sn").val(),
        async: true,
        cache: false, 
        timeout:30000,
        success: function(html){
            alert(html);
        }
    });
}
 
</script>
<form name="tabella"target ="risultati" action="" method="POST">
     <table width="80%" border="0">
     <colgroup bgcolor="#FFFFFF" width="45%" align="right"></colgroup>
     <colgroup bgcolor="#FFFFFF" width="15%" align="right"></colgroup>
     <colgroup bgcolor="#FFFFFF" width="45%" align="right"></colgroup>
     <colgroup bgcolor="#FFFFFF" width="15%" align="right"></colgroup>
     <colgroup bgcolor="#FFFFFF" width="15%" align="right"></colgroup>
 
     <thead>
 
        <tr>
            <td>Matricola</b></td>
            <td><input type="text" name="matricola"></td>
            <td>Stato</b></td>
            <td><input type="text" name="stato"></td>
        </tr>
        <tr>
            <td>S/N</b></font></td>
            <td><input type="text" name="sn"></td>
        </tr>
     </thead>
     </table>
     <input type="button" name="search" onclick="call_ajax()" value="test">
    </form>
pagina2.php
codice:
<?php
            if (isset($_POST['search'])){
                //Recupero i valori
                $campo1 = $_POST['matricola'];
                $campo2 = $_POST['stato'];
                $campoN = $_POST['sn'];
                
                //concateno le query per estrarre la query completa
                $sql = 'SELECT * FROM eltfinal.strumenti WHERE 1=1';
                $sql .= RecuperaFiltro($campo1,'matricola'); 
                $sql .= RecuperaFiltro($campo2,'stato'); 
                $sql .= RecuperaFiltro($campoN,'sn'); 
                $sql .= ";";
                $query= mysql_query ($sql,$connessione);
                //echo '<form target="risultati" action="">';
                echo $sql;
                //inserisco la query in un array
                $array = mysql_fetch_array($query);
                echo $array['matricola'];
                if (!$query)
                {
                print "NO";   
                }
                else
                {
                print "SI";
                }
                //echo '</form>';
            }
            else 
                echo 'non hai premuto il tasto';
        ?>
Prova a dirmi cosa non capisci che ti spiego