Hmm... If copying stuff to RAM causes this problem it could be a number of things, from the psu, faulty cables, overheating etc...
I'd do what I always do in such a case, which is basically remove all add ons (accelerator boards, HDS's etc..) and start from a basic set up adding things back in one by one to see when the fault re-appears...
I't may sound like a long process but in the end you'll usually save a lot of time and head scratching in trying to solve this problem, at least this way you will be able to narrow things to to what may be causing this problem, (personally I'd say the PSU is on the way out) but without doing this type of elimination check it really could be anything...
