Try the following tests.
When your computer speakers are connected to the green "Lineout" you hear
the radio station ?
Computer ----------- amplified_computer_speakers
Now, disconnect the speakers, so the amplified speakers are
no longer connected to the computer. Plug in some headphones.
Now, did the radio station disappear ?
Computer ----------- headphones
If the radio station can no longer be heard, what you're
experiencing is rectification of AM radio station signals
by the input transistors on the amplified speakers. I've had
this happen on my stereo, when an Apple Macintosh is connected
to it. If I connect my PC to the stereo, there is no such
effect. On the Macintosh, the radio station signal appears,
just after selecting "Shutdown" and ending a session. So
the symptoms don't quite match your symptoms, but it is a
similar effect.
If you are close to a powerful AM radio station, that could be
where the signal is coming from.
Being a form of interference, I don't know if I could guarantee
a solution for you. It might take some experimentation
to fix it - it might even require a different set of
computer speakers, if the issue is with the input stage
of the speakers.
Ferrite filters are one solution, but without specs, it is hard
to say what frequency range this device filters. Read the reviews
for the product, to see some successes and failures. If I had to
bet on what was going to provide the most relief from an RF
problem, this is what I'd try.
http://www.radioshack.com/product/index.jsp?productId=2103222
You could try shielded cables, but I would not hold my breath.
(They might not change anything.)
If your computer has TOSLink or SPDIF output on the back, and
the amplified speakers have that kind of input, that would likely
fix it. That is because such a link is digital and immune to
the problems that can affect an audio cable.
For the snap-on ferrite filter, if you wind the wire around the
ferrite core multiple times, that makes the filter more
effective. At least, until the opening in the center is
choked with wire. If you trapped five windings of audio wire
inside the ferrite, it makes the ferrite filter five times
more effective. On this French language web page, you can see
some examples of winding the wires so they go around
the ferrite filter multiple times.
http://www.uska.ch/emv/fr/snap_fs.htm
Paul