It's gonna be tough to build a system that is completely silent.
You can replace the cpu fan and gpu fan with a waterblock. No problems there.
But now you have 2 problems left.
1) The PSU.
What are you gonna do ? Most PSUs have a fan. And that fan makes a little noise. (All fans make noise, no matter what).
So I bought a watercooled PSU. Works very nicely. In fact, the PSU almost does not generate any heat. For a short while (about 2 weeks), when I had just bought a new cpu and gpu, the PSU was the only part in my PC being watercooled. The heat of the cooling system hardly went higher than room temperature.
There is only 1 problem with PSUs. Even without fans, they can make noise. My PSU is emitting some weird high-pitched sound. Not so loud, but because it is so high pitched, you hear it above everything. I've read a bit on the net (and on this website). And supposedly it's the coils inside the PSU. And there is no way to repair/fix that. I paid 200 euros for that PSU a few years back. I don't know when it started to make the noise. The prices have gone up to 250 euros now (280 import in my country even). I'm not gonna pay that for a new PSU every 2-3 years.
2) Airflow through the box.
I've had my PC without any airflow. When I had just bought the watercooled PSU, I had an AMD3400+ and a Radeon9700Pro. Both watercooled. No fans. No airflow. Worked fine for over a year. Then the memory on the R9700Pro melted. The R9700Pro waterblock only covered the gpu, not the memory chips. Modern gpu waterblock cover a lot more than the gpu itself nowadays.
Early this year I upgraded components again. Got a E8500 and a 8800GTX. Both watercooled (with the PSU). No airflow through the box. I kept an eye on temperatures. My hdd went 51C often. My case would heat up. The 8800GTX is known to run very hot. But without airflow, stuff is gonna get hot no matter what.
In the end I activated a casefan. Downvolted it from 12V to 5V. Spins nicely, almost no sound. But the minimal airflow through the case gives lower temperatures for my hdd and other components. At least 10C lower.
My only problem atm: the high pitch in the PSU.
I need to replace it.
I plan to buy a PSU with fan, which also brings a little airflow through the case. I don't need much airflow, just a little. If the PSU causes a little airflow, then I can disable the case fan again. Therefor I'd like to get a PSU with a fan where I can lower the speed. Either with a switch on the PSU, or by downvolting the power going to the fan. Anyone who knows such a PSU ? I don't want it to be done via drivers and software, because I use my system with Linux too.
About the sound of water flowing through the tubes ? I've never heard that. The hdd will be louder. Probably even when it is idle.