i think a fan-cooled PC can be as quite as you need, if done right.. i build mine always fan-cooled, and the noise of the HDs usually masks my fan-noise comletely..
you have to plan the system carefully, but can save quite some money and hassles and risk.
chose components that will not produce big amounts of heat. (i personally usually pick the most powerful
fan-less gfx-card i can get for my machines, for example..)
chose a nice housing for a good airflow. it has to have space for 12 cm fans, 2-3 at the rear-side, 1-2 at the frontside
make the housing airtight all over, only leave fan-area front and rear open.
use 2-3 fans at the rear-side and power them just enough to ensure startup -> veeery slow turning fans will make almost no noise. bigger fans are always quieter than smaller fans.
use a big-surface cooler on CPU. again, use one with a 12 cm fan, lowest RPM
make sure, CPU-fan blows sidewards, in the same direction as the housing-airflow (usually from front to rear)
turn the thing on and observe all the important temperatures. you will propably have sufficient cooling. if your HDs overheat, use 2 additional fans in the front (or better, if there is space, put 1-2 add. fans rear-side), again as slow as possible.
important: ensure a nice airflow, where a lot of air can flow (relatively) slow from front to rear. slow wind produces less noise than strong wind)
avoid any fan with less than 12 cm dia. in your system (also PSU, CPU, GPU!) (smaller, faster fans always produce more noise)
instead of powering fans up, use more, slower fans.
cooling your system in such a way usually only leaves the motors from the HDs audible. these are loud enough to mask the fans. so not any louder than water-cooling.
pls note, cooling this way usually works for eco-designed PCs, that generally don't get very hot.
when you are an overclocker, or using top-end components, you might be better off with a liquid-cooling, because at such high temperatures any fan would have to move alot of air for sufficient cooling. this produces noise at the fan.
please note also, that the above is not an instruction how to do it, but how it could be done. it is my approach for cooling that turned out to work for the rigs i set up.
it takes some experience though, to choose fans and components and housing that best match each other. in the beginning, better be save than sorry, and plan to have one fan more.. then you have to tune your fans down and down, while observing the temperatures. maybe in the end you can again remove one fan
so in the end for noiseless cooling: fan or liquid isn't really a matter of noise, but a matter of the overall system-power and cost. (imo)
fan-cooling:
can be (almost) noiseless.
is cheap.
can only cool a certain amount before starting to make noise.
liquid cooling:
can be (almost) noiseless.
is quite expensive.
has alot more noiseless cooling-power for top-end / overclocked components.
trux