I have an EPIA P4-ITX w/ Celeron 2.4Ghz processor. I've had no problems with my Arise MPD-810 PSU. If you can keep it cool, it can put out around 120W of power. I like it because it is cheap ($79), it has good input voltage range (10V-30V), and has lots of juice on the 5V rail (14 amps) so I can power all my USB devices (I have 6 devices) and my 2.5" HDD without a problem.
But, just to warn you, 10V is cutting it very close to the crank voltage, and many people have had problems surviving crank with this PSU. Luckily, my battery puts out more than 10V during crank, so I've had no problems.
Also, I haven't tried with a P4, but I'm sure that if you get a Northwood based one, power won't be an issue.