OK so here's what I have:
* 1.1GHz Celeron system
* ATI Radeon PCI 9200
* Cheap 6.1 soundcard (with coaxial S/PDIF and that's all I care about)
* 256 MB RAM
* 128 MB CF Card (on IDE bus)
* DVD

Here's what I want:
* Movie player (mplayer)
* Music player (with webradio and all that stuff)
* Web browser
* Samba client to access network shares
* SSH server to remote admin the thing
* A nice frontend would be nice
* it will be connected to a TV via a VGA->RGB Scart adapter cable

I would like some input from people with similar projects. Right now I have DSL installed on it but I don't like it and there's some issues with the Radeon card so I prefer the newest kernel and X11.

A recommendation to which distro I should choose would be a good start. And I'd rather not use LFS or anything that complicated (I have limited spare time for this project). Precompiled binaries is almost required, as the system is very slow. Would it be possible to take out all the "good parts" from an existing Fedora installation and somehow cram onto the CF card, or should I just forget that and go for something readymade? The trouble is, all the flash-sized distros I find use old kernels and old x11. I want the latest, at least a 2.6 kernel and preferably xorg, as I'm having some problems that are probably related to bad drivers.

You have an optical drive so you can run any liveCD that you want.
http://www.efense.com/helix/
http://knopper.net/knoppix/index-en.html
http://www.freesbie.org/

Or put any small free hard drive in it. Slackware or FreeBSD run well if you get a little space.

Thank you for your info, but I might have been unclear about my purposes.
The point is to NOT use a hard drive because I want it to be silent. The optical drive should be used for DVD playback so that is ruled out. The distro must boot from the CF card itself.

How about Puppy Linux? Not sure about the kernel version or X server being used, but that's mentioned quite a lot. Just out of interest though, if you've got a PSU running, and then add a DVD spinning a disc for you, you're not going to hear a hard drive spinning unless you something noisy like an old seagate drive, so why do you have to use a 128MB CF card?

I have a 5400 RPM HD which is supposed to be silent, but it isn't, not to the extent I require for this project. It needs only to be that quiet when NOT playing DVDs (like when playing music or it just sits there idle). The PSU is totally quiet (temperature-controlled fan) and I added a couple of resistors to the CPU fan so it runs almost totally quiet. The system is still quite cool, at least not too hot. Right now the hsync of the CRT tube of the TV is louder than the computer so I'm quite happy with it hardware-wise.

As for Puppy linux, it sounds promising, but has the same problem as DSL: 2.4 kernel, no drivers (has it even got ALSA? DSL hasn't). Maybe it is impossible to make a new linux system fit on a 128 MB root filesystem