how to open a page in new tab on button click in asp.net?

You could use window.open. Like this:

protected void btnNewEntry_Click(object sender, EventArgs e)
{ 
   Page.ClientScript.RegisterStartupScript(
   this.GetType(),"OpenWindow","window.open('YourURL','_newtab');",true);
}

Why not just call window.open straight from OnClick?

<asp:Button ID="btnNewEntry" runat="Server" CssClass="button" Text="New Entry" OnClick="window.open('New.aspx')" />