I want to figure out how to make a PC that's more like a car amplifier: Huge passive heat sink on the outside. No fans, just a silent brick.

Deltatronic does just that. Their Silentium! uses a passive PSU and a heatpipe + convector system to cool the CPU and GPU. According to description one of the side walls of the case has cooling rips. HDD Cage. Also available as a kit. They claim it works for Pentium4s up to 3,06 GHz and probably even future CPUs .