Overcooling?

Can you cool your pc so much that it shuts down?

Can overcooling slow down cpu or gpu performance?

Err... no. If anything, cooling down pc parts makes it work better.

I wish I can run my computer in a space so cold it runs at peak efficiency

Actually, Hard Drives from what I've heard don't run well too cold. Otherwise, everything else is fine!

Technically i think it's possible but PCs have worked perfectly fine when cooled with liquid nitrogen so i doubt you'll hit the limit

Yes you can.

Most of the systems cooled directly with liquid nitrogen only have a small amount in it before they turn it on. Afterwards they apply more and proceed to overclock and contine to apply more as they continue to overclock higher. If you place everything in it at first the CPU isnt likely to turn on.Most places dont show this process because its rather boring and most people are just interested in knowing how high they got.

The extreme cold slows down the flow of electrons. It may slow it down enough to prevent to PC from turning on since its receiving only a trickle of power instead of an initial short burst to get things started.

computers work best in the 16-40 degree ranges.

Too hot or too cold and it will die.

I dont think you can buy a cooler that cools it that much, but if it is operated in 0 degrees celcius it will likely break down. It is a fairly common problem, at science stations in permafrost areas, or places like Greenland. (like weather stations tv stations) Electronics is extremely fragile.