A P4 by itself takes 80W to 110W. Compare that to a via board that totals 11W for the cpu and mobo.
There are many power supply calculators. This is the first after a quick google:
http://www.journeysystems.com/power_...calculator.php
Obviously the P4 is more powerful than any C3/C7, but do you need it? Think of what you will be doing. I can run xvids, and play music, and SNES on the P3 computer I bought 6 years ago. Top of the line 500Mhz, with 32Mb of ram. Origianlly had 98SE on it. I can also run everything on a PII 200Mhz with 16Mb of RAM and a 3Gb HD. albeit it is a bit slower and you can see a noticeable difference in response, but it runs.
P4 will work... but you will only ever squeeze out 3%-10% cpu usage if that high. My C3 board (m10k) stays at around 2%-10% and I hear it is equivalent to a P3 700Mhz-800Mhz. It peaks around 50%, and have yet to have it unresponsive. It switches to and from RR screens instantly, back and forth from video to music to GPS within a blink of an eye (there is a small itty bitty pause of audio and the logo jitters and then it switches to from video, but it is so small that it is only enough for you to see it and then gone). I call that instant.
However you may want to encode video as you drive and play WoW or something, so a P4 may be a good choice. It is all up to how you are going to use it, and how you want to go about it. Keep in mind a DSATX ($$$) is your only DC-DC option, so add that in to the price of that computer or an inverter (bad idea unless a neccessity or laziness). So your $200 computer turns into $400-$500 while a smaller more efficient solution even like the Pentium M would use a smaller cheaper PSU and cost around the same. For extremeness and good power rates, check out the new Core Solo's and Core Duo's. More efficeint than Pentium M's, yet soooooooo much more powerful. They even make an itx mobo for it, although it is in the mid $300's.