Is it possible to run a motherboard in distilled water?

I've done it. Don't do it.

I set up a computer in an acrylic case with good quality distilled water and a cheap motherboard as a test, with heatsinks only (no fans/moving parts). I cleaned the inside of the case with isopropyl alcohol, thinking that would remove any existing contaminants.

Within a day or two, I noticed that all the contacts/metal parts on the board began to rust. Even the stainless steel on the case of the SSD had begun to rust. Another day later, the motherboard died. When I removed the motherboard, being the first time anything physically removed (no fans), a huge cloud of rust particles came off and turned the water a lovely brown color.

Stick with something that metal parts can be friends with, like mineral oil.

Yes it is. Running a computer in distilled water is no issue.
However, keeping the water distilled is near impossible.

As soon as contaminants pollute the water even in very small amounts, the water will begin to corrode and given enough ionic contaminants, the water will stop being an insulator and become a very good conductor.

This kills the computer.

Now various people will say different things with regards to the amount of time it takes for the water to become contaminated enough to cause problems but in almost all cases it is within weeks in sealed environments, days in open.

Mineral oil is a far better alternative for a submerged build.