u need proper shielding and grounding.

u say your cables are cheap cables. try getting better ones and see whether the problem goes away.
if the problem still persists, then the circuitry in your guitar is the one causing the problems. its not being grounded properly.

u say u touch it then the sound disappears right?

thats grounding problem. maybe your amp is not being grounded properly.

2 pin power plug?

means its not being grounded properly. er i dont think there's really any way around this since the amp is built that way.

actually, another source of problem is the power source. have u tried changing plugs? if the power is not clean, the lack of grounding will allow the noise to go up all the way to your amp, and all the way to your guitar too.

i guess u can change it to a 3 pin plug.
but if your cable doesnt have an earth wire, its no point right?
u can just put it there, but there is no grounding which defeats the whole purpose of having a 3pin socket.

haha i believe its the grounding issue. did u try using the amp in another room yet?

since your cables are better grounded now, it will help in the reduction of the noise. i believe there is no way around it, as far as my limited knowledge.