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If both machines are running Linux, then you could use ssh to login to your Music machine and play the files that way. You could use some remote software such as VNC.
You could also use XMMS to play your media files, then you could use SSH to login and use xmms-client (or whatever it's called), or you could use the XMMS-Web thingy that provides a web-based frontend to your XMMS.
There are other methods, but they're the ones that spring to mind.