The solution for this is to change the page so it will not override the menu place holder, but inherite it from the Master Page. The place holders we are interested in are: "PlaceHolderLeftNavBar" and "PlaceHolderNavSpacer".
Start by opening the SharePoint Designer. Open the webpart page or basic page you want to add the menu to. In code view look for the following lines and delete them:
<asp:Content ContentPlaceHolderId="PlaceHolderLeftNavBar" runat="server"></asp:Content>
and
<asp:Content ContentPlaceHolderId="PlaceHolderNavSpacer" runat="server"></asp:Content>
and
<SharePoint:UIVersionedContent ID="WebPartPageHideQLStyles" UIVersion="4" runat="server"><ContentTemplate>
<style type="text/css">
body #s4-leftpanel {
display:none;
}
.s4-ca {
margin-left:0px;
}
</style>
Save the file. You will get a warning saying you are about to customize the page. Just go ahead.
Hope this saves time.