Можно ли запустить материнскую плату в дистиллированной воде?

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.

I would be highly surprised if it actually worked, even for a second. Motherboards have some pretty high frequencies, and the PCB routing is intricately designed to minimize capacitance so that they can actually carry these signals.

Changing the fluid that is around the board from air (dielectric constant = 1.00059) to water (80.4) is likely to introduce a lot of capacitances that weren't designed for and would be way out of tolerance, especially for channels like CPU to RAM. The additional capacitance just wouldn't allow the signal to switch fast enough to be able to reliably transmit the data. By the way, mineral oil has a dielectric constant of 2.1, so much less capacitancy than water, and some people have had success with submersion in that.

If you would be doing this so that you can overclock everything, then the higher dielectric constant works against that by reducing the maximum frequency that the board can operate at.

The Cray computers didn't have nearly the same challenges to being submerged, since the highest fundamental frequency signal on the board was 125MHz, and modern machines potentially have ~4000MHz signals, with common RAM being just below 2000MHz, with harmonics extending to >5x the fundamentals to form the waveform accurately.

I agree with the others here that have noted that metals are slightly soluble in water (especially copper), so the water would start to become conductive immediately. Voltage differences would also cause electrolysis through the water and H2 + O2 would be produced, as well as forcing ions into aqueous solution.

I cannot speak to the use of water but a liquid cooling system was implemented years ago using fluorinert. This was done on the cray 2 and 3 I believe. The following snippet can be found on wikipedia. I did have the opportunity to see the cray-3 running in a tank of fluorinert completely submerged in liquid much like a fish tank.

The cards were packed right on top of each other, so the resulting stack was only about 3 inches high. With this sort of density there was no way any conventional air-cooled system would work; there was too little room for air to flow between the ICs. Instead the system would be immersed in a tank of a new inert liquid from 3M, Fluorinert. The cooling liquid was forced sideways through the modules under pressure, and the flow rate was roughly one inch per second. The heated liquid was cooled using chilled water heat exchangers and returned to the main tank. Work on the new design started in earnest in 1982, several years after the original start date.

It would seem that pure water would not cause any electrical problems given its insulative properties, and it's further suggested that you would want deionized water, but the problems that arise are only partly due to the introduction of contaminants (e.g. minerals, salts, metals, etc.). Even if you could guarantee that no contaminants entered the water, problems are inevitable on account of the autoionization of water. Neutral water does not remain neutral.

As the water (in conjunction with oxygen which is always in water, taken from the air to some equilibrium) would corrode metal parts, you have to prevent the metal parts come in direct contact with the water.

This can be done by painting of the components in some water resistant finish. There are several coatings out there exactly for this purpose, protecting electric components from water. Although this paints are meant for occasional dew, some of them work quite well for total submergence.

You just have to made sure your finish doesn't break contacts that are needed (just spray paint after connecting all plugs needed) and doesn't stop cooling (eg. keep the paint off the CPU heatspreader or sand it to a very thin layer there).

While some special praised paints doesn't seem to provide a long term protection (see here: http://hackaday.com/2013/12/26/neverwet-on-electronics/ ), more simple plastic sprays or expoxy based resin paints may do if the layer is thick enough.

H2O 

does not conduct electricity, however distilled water is more like

H2O <-> H20 + H + OH 

Actually the % of the ions is really low

just 10^-7

So every about 10.000.000 molecules of water you have also a H and a OH ion. (If I remember correct my studies over pH, in case I'm wrong just let me know I'll refresh some book or look at wikipedia)

but enough to cause troubles in the long/short run (depending on intensity of current and magnetic fields)

And here you need just a minimal differential of potential to cause water be subject to electrolisis, hence the ions will be pulled out of water thanks to the magnetic field and will react with metal parts.

So actually you have ions inside water that can still carry charge (and so electricity, even if low currents), and despite that any magnetic field, even minimal will cause ions to separate from water and hence attack any metal part (beacause also parts in different metals act as catode-anode)

In reality water is corrosive for metals even without currents (well technically the metals will create a current even if not plugged into a power source), but current can accelerate/mitigate the corrosion (of course since computer parts are not designed for that, it is likely that a computer part would provide the exact current to counter the corrosion and hence will corrode.