So. Just to continue testing, I did the following. I turned the amplifier off. I used the "Line out" of the multieffect with a headphone. No result, the noise (the quasi-stochastic noise) was still there.

To check this ground loop effect, I disabled it. I disconnected my PC, and the amp from the mains. No effect, the noise was still there.

Don't think about this as a "hum"-like noise. It is not always present. I know that it will come, but I don't know when. After that I know that it'll be a daaamn loud noise for a while, but I know that it will disappear. NOT FADE, just simply disappear.

So I'll go through my cables once again. I have no idea. Maybe my wah is really faulty somehow.