<table class="small">
            <caption>Закодировать товар:</caption>
            <tr><td class="forml th_w3">На склад:</td>
                <td class="formr"><asp:DropDownList ID="DDL_ShopBox" runat="server" Width="100%" DataTextField="shName" DataValueField="shID" EnableViewState="true" AutoPostBack="true" OnSelectedIndexChanged="DDL_ShopBox_AutoPostBack" /></td></tr>
            <tr><td class="forml">Коробка:</td>
                <td class="left"><asp:RadioButton ID="RB_NoTara" runat="server" GroupName="tra" Text="Без" />
            <tr><td class="forml nowrap"><asp:CheckBox ID="CursorBox" runat="server" Checked="false" ToolTip="Курсор по умолчанию" Text="Серийный №: " /></td>
                <td class="formr"><asp:TextBox ID="SerialBox" runat="server" Width="99%" onkeypress="SetSerial(this);" /></td></tr>
            <tr><td class="formlRF">Штрих-код:</td>
                <td class="formr"><asp:TextBox ID="ShtrihBox" runat="server" Width="99%" onkeypress="SetSerial(this);" required="required" /></td></tr>
            <asp:PlaceHolder ID="KolHolder" runat="server" Visible="false">
                <tr><td class="formlRF">Кол-во:</td>
                    <td class="formr"><asp:TextBox ID="KolBox" runat="server" Columns="7" MaxLength="5" min="1" max="32767" type="number" step="1" required="required" /></td></tr>
            </asp:PlaceHolder>
        </table></div>
        <asp:Button ID="SaveButton" runat="server" Text="Записать" OnClick="SaveButtonClick" TabIndex="2" /><br/>
        <script type="text/javascript">
        function SetSerial(curItem) {
            var NextItem;
            if (curItem.id == "<%=SerialBox.ClientID%>") {
            NextItem = "<%=ShtrihBox.ClientID%>";
            }
            if (curItem.id == "<%=ShtrihBox.ClientID%>") {
                NextItem = "<%=KolBox.ClientID%>";
            }
            if (curItem.id == "<%=SerialBox1.ClientID%>") {
                NextItem = "<%=ShtrihBox1.ClientID%>";
            }

            if (event.keyCode == 13) {
                var shBox = document.getElementById(NextItem);
                shBox.focus();
                shBox.select();
                event.returnValue = false;
                return false;
            }
        }
        </script>

event = event || window.event;

...
event = event || window.event;
if (event.keyCode == 13) {
...

onkeypress="return SetSerial(this);"