lethargic_man | How to get rid of mains (?) hum?

I've had the intention for a while of transferring all the music I have for my Hybrid Music System to epicyclic, and then burn it to CD-ROM, before the hardware it runs on (1987-vintage BBC Master and 1986-vintage Music 500) complete packs up. A year ago I had an attempt, but ran into problems with what I thought was mains hum.

compilerbitch suggested plugging everything into the same mains socket, so, finally having got around to moving the pedestal housing my stereo, CD player and Beeb across the room (and getting and tacking down longer speaker wire so I could connect the first of these back to the speakers on the side they had come from), I tried this out... and found the situation unimproved. My father suggested cutting the earth contacts on the Music 500 output, as I'd probably got a mains hum loop, but that made no difference either.

The funny thing is that when I simply play the Music 500 through epicyclic, it plays fine (there's a small amount of background noise, about as much as a computer fan); it's only when I try and capture the sound to record it (using Audacity) that the bad noise turns up (71k MP3). I've tried various techniques on Audacity for getting rid of it, but they always result in a degradation of the sound quality (60k MP3); better would be to eliminate the noise from the input. Anybody got any idea why I only get it when I try to capture the audio?

(Also, when I tweak the Alsa volume controls, there's a master control for playback; there's also a PCM one, and increasing that increases the noise dramatically. Increasing the line-in control also increases the noise when listening to straight play-through, but I've a feeling Audacity bypasses this.)