I use a set of Wharfedale amplified speakers via mini-jack to play
music from my computer. I have noticed that the speakers are humming
when the power is turned on - even if the mini-jack is plugged into
anything. This humming is annoying because it is rather loud -- well,
not loud as in loud but as in not-quiet.

I must fix this humming because it is annoying!
What tips can you give me to get rid of this humming?

I suspected the cable between speaker and player to be the culprit,
because the mini-jack was not original but had some poor-looking
soldering. The cable itself seemed fine, but rather than soldering on a
mini-jack, I decided it would be better to use a factory-made
Sennheiser cable with mini-jack already attached, which I then soldered
onto the board inside the powered speaker. But it still hums just as
loud as before, so this was not the problem in the first place. Who
knew.

What else can I do, apart from throwing away rather good(?) speakers
and buying new ones?