Besides the soundcard.... does the computer itself

does the computer itself make any difference in sound quality?

any components in the computer make any difference?

Intel celeron and pentium 4 make any difference?

more memory produce better sound?

the celeron and p4 should make everything worse. go with a 64 bit AMD processor which is more advanced :)

seriously, none of the listed components should make any difference in sound quality.
Some people think that external "sound cards" are better than ones inside the computer. Due to less electrical noise from the PC components. I'm talking about external units that hook up via USB or Firewire ports. Personally I haven't had any experience with those external devices.

I'd stay away from Celeron processors as they're just not as powerful as a P4 or AMD chips. But that's not based on how it sounds, just how fast and how well the computer works. AMD have generally been more focussed on gaming applications so are more geared towards audio and visual appplications than Intel chips.
Oh yeah, and if you add the Mo-Pingo Puc's it will improve the sound. :)

They do make a tube sound card out there, but I think I leave the tubes and their heat in the basement where they can warm the ambience of the concrete walls.

If you have a digitial noise problem, due to a cheesy power supply, that can make a difference, shielding of the PS could help.

The processor speed can cause glitches, and speed of your modem if you stream audio will be a factor, but frankly if your streaming audio, quality is not a word I associate with that sound. If your using it as a server or CD player it's different. More significant will be the amplifier section. I would try and pick up an outboard amp, and leave the high voltage outside the PC.

Does the poer supply have any effect? Some have tighter voltage specs than others.
If you use a PCI card, the answer is yes. If you use an outboard USB to S/PDIF converter with it's own power supply, no. The issue is PC clock and PC power.
It really takes very little computing horsepower to play back audio, especially if you aren't doing any fanciness with equalizers or crossfades. But if you're using your machine for heavy number-crunching and playing audio files at the same time, you could have some problems. I've had some pretty nasty ground loop problems, running audio from the line-out. None of those problems with an external USB DAC, though the sound quality hasn't just blown me away. How you convert from digital to analog, where that conversion takes place, how whatever signal goes from the PC to the amp will make a big difference. The specs of the PC used, above a fairly low threshold, should not.