I haven't heard of anything that will do what you're looking for. The video streamers can play audio without the TV being turned on, but you'd likely have a hard time doing any navigation other than track skipping and seeking.

The Squeezebox and Squeeze Center (the server software) are by far the best music streaming solution around. It's still got a lot of shine being applied by its developers, but nothing else can really match its feature set at any price.

I'd probably suggest going with two devices if you need something now. It's possible that Logitch will one day release a device that combined its Squeezebox music player with a video streamer, but it's definitely not a sure bet.

For music, as mentioned, the Squeezebox series of products is the top choice. And for video, everything points to Popcorn Hour being miles ahead of anything else.