Just looking at the big picture here.... is this "media pc" going to be a hometheater computer?
If so, are you going to hook it up to a real sound system? If you are, your receiver will be able to play am/fm, and you could get a really cheap CD player / DVD player with mp3 support that will play.
I think having a computer than can have a cd drive that can read without the computer on and output to a soundcard that's working without the computer on would be quite a task. They might make something like that, but I haven't seen it.
As for cassette deck, I think you're totally stuck with getting a real player and connecting it to your computer or receiver.
In my own situation, my computer has kind of become another input device rather than the center of attention it used to be in my system. A receiver is perfect for what you're planning as it will have plenty of inputs that will allow you to switch between inputs and the computer doesn't need to be on to do anything other than when it's the input you want.
I don't know if this is what you had in mind, but personally I couldn't go back to a system without a receiver (or pre-amp / processor) now that I'm used to it.
I guess it comes down to your budget and what you were planning on using for your sound system.
A really cheap route would be to get an A/V switcher and hook that up to your speakers (I'm assuming now that you're using some computer speakers). You could use a really cheap portable radio with line-out (or headphone out) for the radio, a really cheap DVD player for music, and a tape player. If you get an A/V switcher with four inputs, that would allow you to switch between the different source devices without having the computer on.
I don't know if I'm on the right track at all for what you're planning.
I think there are a couple small form factor PCs that come close to what you want to do. I remember a really ugly orange one that I want to say is made by MSI or ASUS? I really didn't pay too much attention to them, but I think that might be a good thing to look into if you're looking for a computer solution.
EDIT: not the one I was thinking of, but
example
EDIT2: oh, and that's not an A64 based one either, so I don't mean you should get that one specifically.