it's all true!!
unfortunately you can't avoid the stuff that's causing the problem.
keep leads as short as poss (as ghostbusters say) don't cross the leads.
you could try ferrite rings
http://www.maplin.co.uk/free_uk_delivery/Ferri te_Rings_29788/Ferrite_Rings_29788.htm
which may help (at least they are cheap)
and of course ... the most expensive utp oxygen free copper cable you can afford
as for the ground ... ideally you want a fully bonded earthed loop to all your kit. (connected to mains earth AND a water pipe)
oh and testing the mains socket won't go amiss either.
I know that it's neither practical or possible to do all this .... a good earth is your best bet (if you can ... clip to a radiator as well)