Without a ton more information on your set-up / settings it is difficult to troubleshoot.
Are you using dual monitors? Is your opposite monitor (from the timeline) the one you want to use? Do you have "Digital Cinema Desktop Preview - Full Screen" selected in the "View/Video Playback" dropdown? I am playing out an HDV clip right now (1080i60 / 59.94 fps / HDV 1080i60 Compressor / 48k Stereo Audio) and it plays just fine on my second desktop monitor at full screen (plays it back in letterbox as my second monitor is not full HD). It works in both "Digital Cinema Desktop Preview - Full Screen" and "Digital Cinema Desktop Preview".
Again...kinda hard to tell you anything without more info on your set-up.
When life gives you dilemmas...make dilemmanade.