With an OpenStreetMapProvider or BingMapProvider, the RadMap at run time was blank, empty, and gray each time I loaded my Silverlight application in a web browser.
I found the cause to be that I loaded my Silverlight application in a web browser with a file-based address, such as "file:///C:/TestPage.html".
The solution was to start IIS Express, host my Silverlight application on localhost in IIS Express, and load my Silverlight application in a web browser with a web-based address on localhost, such as "http://localhost:8080/TestPage.html".
I hope this helps other people with the same problem.
Problem with Map at runtime