Nessun conflitto.
Se usi il metodo GET, l'attributo action del form viene sovrascritto per passare i campi del form.
Esempio, il form:
codice:
<form action="search.php" method="get">
   <input name="A" value="1">
   <input name="B" value="2">
   <input type="submit" value="invia">
</form>
ti porterà, quando inviato, a:
search.php?A=1&B=2

Nel tuo caso, per passare dei parametri "statici", puoi usare dei campi hidden:
Codice PHP:
<form action="home.php" method="get">  

<input type="hidden" name="page" value="search">
<input type="hidden" name="lim1" value="<?echo $lim1;?>">
<input type="hidden" name="lim2" value="5">

                                    <table cellpadding="0" cellspacing="0">  
                                        <tr>  
                                            <td valign="top">  
                                                <input type="text" name="string" id="string" value="<?echo $string;?>" style="height: 34px; width: 400px; font-size: 30px;-webkit-border-top-left-radius: 7px;-webkit-border-bottom-left-radius: 7px;-moz-border-radius-topleft: 7px;-moz-border-radius-bottomleft: 7px;border-top-left-radius: 7px;border-bottom-left-radius: 7px;" autocomplete="on">  
                                            </td>  
                                            <td valign="bottom">  
                                                <input type="image" src="image/src.gif" height="40" width="40" id="cerca" autocomplete="off">  
                                            </td>  
                                        </tr>  
                                    </table>  
                                </form>