How do I shield my pc-speakers from mobile interference?
It sounds like the price was more a function of the brand name than good design.

There are two possibilities: The noise is coming in via the audio cable or into the circuitry of the amplifier directly over the air.

The first is relatively easy to deal with.  Try putting a 100pF or so ceramic cap accross the audio leads going into the speaker system as close to the case as possible.  Check the cap datasheet and choose one with as high a useable frequency range as possible.  If RF from the cellphone is getting in via the cable, then this can get rectified and otherwise partially demodulated by circuitry designed to handle five orders of magnitude lower frequencies.  The 100pF cap should shunt most of the RF before it can cause trouble.  You'll need one such cap on each audio feed, which is two of them if this is a stereo system.

If the capacitors doesn't help, then it gets more complicated since the circuitry in the box is apparently picking up the cellphone signal directly.  To verify this, try wrapping the speaker box in alumninum foil that is connected to ground at the audio input jack.  Only connect it at that one place.  If that's what is required to fix the problem, then you'll have to add a shield somehow.  You can keep the external aluminum foil if you don't care what it looks like.  Otherwise you will have to open the box and add your own shield internally.

Or, you could sell the Logitech speakers and buy a cheaper pair that works better and even get some money back in the process.