To make sure i understand, you want to grab Kentico content (on a page) from a Non Kentico site and pull it in?
There's a couple ways to do this. If you purely want to grab the webpart's content (html), what i would recommend is use my "Webpart to Api Tool" in the marketplace. You can point it to the web part you want the content, and the tool will clear the entire page except for that content and 'spit it out' for you.
You may need to adjust the Visibility on the Converter to a macro like {% !string.IsNullOrWhiteSpace(QueryString.GrabWebPart) && QueryString.GrabWebPart=="MyWebPart" |(identity)GlobalAdministrator%} so you can call from the external page "cmsdev.ingrammicro.dmz/cms/Content-Pages/TestPage.aspx?GrabWebPart=MyWebPart" using an jquery AJAX Call and just place the return data (the html) where you want in the page.
The Webpart to API Converter's only 'flaw' is currently it doesn't work on cached widgets/webparts, so just disable caching on it.