Use CustomValidator in place of RequiredFieldValidator so no require to use of ValidationSummary control
Pl follow below code for use requirement.
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<head runat="server">
<title>Untitled Page</title>
<script src="../Script/jquery-1.6.2.js" type="text/javascript"></script>
<script type="text/javascript">
function CheckValidGrid(source, args)
{
var fire =true;
for(var i=1;i<$("#grddata tr").length;i++)
{
if($.trim($("#grddata tr:eq("+i+") input:[id*='txtCategoryName']").val())=="")
{
fire =false;
break;
}
}
if(!fire)
{
args.IsValid = false;
alert("Please enter value for all new category name");
}
else
{
args.IsValid = true;
}
}
</script>
</head>
<body>
<form id="form1" runat="server">
<div>
<asp:SqlDataSource ID="SqlDataSource1" runat="server" ConnectionString="<%$ ConnectionStrings:ConnectionString %>"
SelectCommand="SELECT [CategoryID], [CategoryName], [Description] FROM [Categories]">
</asp:SqlDataSource>
<asp:GridView ID="grddata" runat="server" AutoGenerateColumns="False" DataKeyNames="CategoryID"
DataSourceID="SqlDataSource1">
<Columns>
<asp:BoundField DataField="CategoryName" HeaderText="CategoryName" SortExpression="CategoryName" />
<asp:TemplateField HeaderText="New Category Name">
<ItemTemplate>
<asp:TextBox ID="txtCategoryName" runat="server"></asp:TextBox>
</ItemTemplate>
</asp:TemplateField>
</Columns>
</asp:GridView>
<asp:CustomValidator ID="cstValidate" ClientValidationFunction="CheckValidGrid" runat="server"></asp:CustomValidator>
</div>
<div>
<asp:Button ID="btnsave" runat="server" Text="Save" />
</div><pre><pre lang="HTML"></pre></pre>
</form>
</body>
</html>