@JAKUS - you may want to evaluate your inter-personal skills a bit
@Firenze, from all the to'ing and fro'ing I could make out on here, your CPU voltage seemed higher than normal, and when underclocked your system was fine and played the games fine, just the odd bit of artifacting on-screen?
You've sailed through memtests and those have turned out fine from what I read above, so check that off the list. If you can, any chance you could check the voltage running through your 5870, and the corresponding core and memory clocks. Personally, I think as mentioned somewhere in the mess above, you may have a little bit of a "naff" card that might need either a) more volts pumped through or b) underclocking a little bit, more-so on the memory rather than the core.
Let us know how you get on.
And JAKUS is like tequila, take it with a pinch of salt