RadWindow loads its content page only when it is first shown. Thus, if the page has a proper reference to jQuery, the alert should fire. Could you try loading the same content page in a simple iframe through its src attribute to see if the alert fires as expected? If not, then the issue would be somewhere between the iframe and jQuery and not lie with RadWindow.
Also, can you confirm there are no script errors in the browser console, as this can prevent scripts from running?
Another thing I can suggest is setting the ReloadOnShow property of the RadWindow to true, so each time it opens it will append a random querystring to the page URL so you will always have a GET request for the content page.