Do mean MP3 file, not MPEG? If so, have you tried using the “Import” function from your “File” pull-down menu (or the keyboard shortcut)? When I have had problems dragging things into bins to import them, sometimes this works a bit better.
Any reason it would have played just fine last week, but not now? I transferred the media to an internal drive and got the same results. Could the size of the file have anything to do with the issue? (It was a single 45-minute piece of video.)