You really need screened twisted pairs. Not easily available. I did manage to get away with using telephone cable, two grounds commoned and one wire for each signal over a 10M run. As you have found hum present, I wonder if there is an earthing problem between the two rooms. There should not be any significant hum from pick up. The other possible problems causing hum and distortion are that the output and input impedances are not matching. Check what the values are and if in doubt, try terminating the amplifier input with 1K Ohms across each input as a start. Also check that the computer output is not at too high a level. I'd expect the amplifier to work with 1V rms at most, frequently less.
Regards Capitol