Here’s my steps and workarounds from the very beginning (in Visual Studio 2012), hopefully some part of this will help fix whatever error you are encountering.

File -> New Project
.NET Framework 4.5
Visual C# -> Web
ASP.NET Web Forms Application
Add AjaxControlToolkit version 7.0123 (dll is actually 4.5.7.123 which is January 2013 I believe) via NuGet

Open Default.aspx
Add a calendar to the BodyContent / MainContent:

<asp:TextBox ID="myTextBox" runat="server" />
<ajaxToolkit:CalendarExtender ID="myCalendar" runat="server" TargetControlID="myTextBox" Format="dd/MM/yyyy" />

Run it up (F5 will do)

It might error about ASP.NET Ajax 4.0 scripts:
0x800a139e – JavaScript runtime error: AjaxControlToolkit requires ASP.NET Ajax 4.0 scripts. Ensure the correct version of the scripts are referenced. If you are using an ASP.NET ScriptManager, switch to the ToolkitScriptManager in AjaxControlToolkit.dll.

I’ve also seen it error about:
‘MsAjaxBundle’ is not a valid script name. The name must end in ‘.js’.

No bother, let’s remove that reference from the Site.Master, so:

<asp:ScriptManager runat="server">
    <Scripts>
        <%--Framework Scripts--%>
        <asp:ScriptReference Name="MsAjaxBundle" />
        <asp:ScriptReference Name="jquery" />
        <asp:ScriptReference Name="jquery.ui.combined" />
        <asp:ScriptReference Name="WebForms.js" Assembly="System.Web" Path="~/Scripts/WebForms/WebForms.js" />
        <asp:ScriptReference Name="WebUIValidation.js" Assembly="System.Web" Path="~/Scripts/WebForms/WebUIValidation.js" />
        <asp:ScriptReference Name="MenuStandards.js" Assembly="System.Web" Path="~/Scripts/WebForms/MenuStandards.js" />
        <asp:ScriptReference Name="GridView.js" Assembly="System.Web" Path="~/Scripts/WebForms/GridView.js" />
        <asp:ScriptReference Name="DetailsView.js" Assembly="System.Web" Path="~/Scripts/WebForms/DetailsView.js" />
        <asp:ScriptReference Name="TreeView.js" Assembly="System.Web" Path="~/Scripts/WebForms/TreeView.js" />
        <asp:ScriptReference Name="WebParts.js" Assembly="System.Web" Path="~/Scripts/WebForms/WebParts.js" />
        <asp:ScriptReference Name="Focus.js" Assembly="System.Web" Path="~/Scripts/WebForms/Focus.js" />
        <asp:ScriptReference Name="WebFormsBundle" />
        <%--Site Scripts--%>

    </Scripts>
</asp:ScriptManager>

Now becomes:

<asp:ScriptManager runat="server">
    <Scripts>
        <asp:ScriptReference Name="jquery" />
        <asp:ScriptReference Name="jquery.ui.combined" />
        <asp:ScriptReference Name="WebForms.js" Assembly="System.Web" Path="~/Scripts/WebForms/WebForms.js" />
        <asp:ScriptReference Name="WebUIValidation.js" Assembly="System.Web" Path="~/Scripts/WebForms/WebUIValidation.js" />
        <asp:ScriptReference Name="MenuStandards.js" Assembly="System.Web" Path="~/Scripts/WebForms/MenuStandards.js" />
        <asp:ScriptReference Name="GridView.js" Assembly="System.Web" Path="~/Scripts/WebForms/GridView.js" />
        <asp:ScriptReference Name="DetailsView.js" Assembly="System.Web" Path="~/Scripts/WebForms/DetailsView.js" />
        <asp:ScriptReference Name="TreeView.js" Assembly="System.Web" Path="~/Scripts/WebForms/TreeView.js" />
        <asp:ScriptReference Name="WebParts.js" Assembly="System.Web" Path="~/Scripts/WebForms/WebParts.js" />
        <asp:ScriptReference Name="Focus.js" Assembly="System.Web" Path="~/Scripts/WebForms/Focus.js" />
        <asp:ScriptReference Name="WebFormsBundle" />
    </Scripts>
</asp:ScriptManager>

Next is ToolkitScriptManager, the snippet above now becomes:

<ajaxToolkit:ToolkitScriptManager runat="server">
    <Scripts>
        <asp:ScriptReference Name="jquery" />
        <asp:ScriptReference Name="jquery.ui.combined" />
        <asp:ScriptReference Name="WebForms.js" Assembly="System.Web" Path="~/Scripts/WebForms/WebForms.js" />
        <asp:ScriptReference Name="WebUIValidation.js" Assembly="System.Web" Path="~/Scripts/WebForms/WebUIValidation.js" />
        <asp:ScriptReference Name="MenuStandards.js" Assembly="System.Web" Path="~/Scripts/WebForms/MenuStandards.js" />
        <asp:ScriptReference Name="GridView.js" Assembly="System.Web" Path="~/Scripts/WebForms/GridView.js" />
        <asp:ScriptReference Name="DetailsView.js" Assembly="System.Web" Path="~/Scripts/WebForms/DetailsView.js" />
        <asp:ScriptReference Name="TreeView.js" Assembly="System.Web" Path="~/Scripts/WebForms/TreeView.js" />
        <asp:ScriptReference Name="WebParts.js" Assembly="System.Web" Path="~/Scripts/WebForms/WebParts.js" />
        <asp:ScriptReference Name="Focus.js" Assembly="System.Web" Path="~/Scripts/WebForms/Focus.js" />
        <asp:ScriptReference Name="WebFormsBundle" />
    </Scripts>
</ajaxToolkit:ToolkitScriptManager>

But of course this fails with:
Could not load file or assembly ‘System.Web’ or one of its dependencies. The system cannot find the file specified.

Remove the Assembly=”System.Web” part from the ScriptReference so we have have:

<ajaxToolkit:ToolkitScriptManager runat="server">
    <Scripts>
        <asp:ScriptReference Name="jquery" />
        <asp:ScriptReference Name="jquery.ui.combined" />
        <asp:ScriptReference Name="WebForms.js" Path="~/Scripts/WebForms/WebForms.js" />
        <asp:ScriptReference Name="WebUIValidation.js" Path="~/Scripts/WebForms/WebUIValidation.js" />
        <asp:ScriptReference Name="MenuStandards.js" Path="~/Scripts/WebForms/MenuStandards.js" />
        <asp:ScriptReference Name="GridView.js" Path="~/Scripts/WebForms/GridView.js" />
        <asp:ScriptReference Name="DetailsView.js" Path="~/Scripts/WebForms/DetailsView.js" />
        <asp:ScriptReference Name="TreeView.js" Path="~/Scripts/WebForms/TreeView.js" />
        <asp:ScriptReference Name="WebParts.js" Path="~/Scripts/WebForms/WebParts.js" />
        <asp:ScriptReference Name="Focus.js" Path="~/Scripts/WebForms/Focus.js" />
        <asp:ScriptReference Name="WebFormsBundle" />
    </Scripts>
</ajaxToolkit:ToolkitScriptManager>

It seems the new web forms project template adds ‘Microsoft.AspNet.ScriptManager.MSAjax 4.5.6′ package, this appears to conflict with the toolkit, so remove this via “Manage NuGet Packages”
Visual Studio might still leave the dll in your bin directory even after a clean, make sure you manually clean that out.