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overhead of maintaining a gui front-end. Try mplayer.

> 0) many times when I just try to play something
> mplayer cannot open "/dev/dsp"/audio device. So I have
> no sound. Sometimes it works. I do not understand this
> as xmms always works (maybe it takes a minute to
> start, but it works)

Are you running KDE, by chance...? Sounds like mplayer is having trouble 
grabbing /dev/dsp from artsd. You could try using arts as the output device, 
although in my experience this slows things down compared to using native oss 
or alsa. Having said that, you should have ample power with a P4. My Celeron 
300 / Neomagic-2160 laptop can just about play DVD content with heavy 
tweaking.

> 1) The first attempt for playing a dvd results in a
> play mode which does not play (black screen, no
> sound).
> ...
> 2) The second attempt works seemlessly :-??????
> 3) The video replay, if it works is much too SLOW.
> I guess I get about 2 frames per second.

Hmm... Perhaps try a different video output device? (Which one are you using?) 
I don't know which ones work properly with nVidia's drivers but you could try 
the xv device.

Regards
Stephen