Handbrake supports most common audio and video files, however, open source applications usually contains bugs. My advice is to try to close the application and then open it again with Administrator access then drag the file or use the File > Open. This could also be a small bug while using drag and drop, because as I've said earlier, the application supports most common file types including the ones you've already tried.
Additionally, re-install the product and obtain the Combined Community Codec Pack Free through the application's page on Software Informer and the program will use the 3rd party codecs instead of the ones deployed with the main application.