So imagine you had a computer floating out in space. Is it easier or harder to cool a system? It's much colder (assuming no radiation) but there is almost no atmosphere for convection.

http://www.spacefacts.de/mission/english/skylab-2.htm

Hard to cool in space. Hence the need for foil shades to keep the sun off.

^ This is correct. Satellites need a special paint coating that helps them radiate internal heat away, while minimizing radiation taken in by the satellite. Too bad, since a computer in a complete vacuum (and suspended magically) would be the closest thing to being totally, absolutely silent

Satellites are in the earth's orbit and get radiation from the sun. Suppose this is deep space and it has layers of mylar blocking radiation from stars. Can a heatsink transfer heat away if there is no atmosphere?

Yes. Look up "black body radiation" in your favorite search engine.