I actually had a slightly lower set of the radeon cards and was having pretty much the same issue. Mine were crossfired Radeon HD 5770 1GB 126-bit. And I was having horizontal lines that were multi colored as whatever I was doing froze up and shortly after my pc rebooted. No bluescreen, just randomly rebooting. However, ever since I got my new Radeon 7850, I've been having bluescreens left and right as well as random freezing. So one thing you may want to also look into is the ram and the motherboard. I'll be having mine tested in the next few weeks to see which is the cause of that issue.

May also look into seeing about my amps on my psu to see if its higher than 10A or not.

Sorry you're still having trouble xavi. It seems that there are many variants of this problem and the radeon 5XXX series is just really touchy in general. 

Keep us all posted on your progress. I want to continue brainstorming with the folks on here and other forums to figure out more about these crashes. One thing I will say though is that throughout this gargantuan struggle I have learned a LOT about video cards, what with all the bios flashing and cooling methods and everything else we've tried!

Apple Cinema Display A1081 20" 1680 x 1050 (60 Hz)
Windows 7 Home Premium x64
ASUS M4A785TD-V EVO Mobo
AMD Phenom II X4 965 @ 3.4 GHZ (+ Hyper 212 Evo HSF)
AMD ATI Radeon HD 5870 1GB
8 GB DDR3 @ 1333 GSKILL
OCZ ModXStream Pro 600W modular psu

Try 12.4 drivers just to see if it works.

I think it's stable with 650/1000 now. No crash since I underclocked the card. I'll refrain from messing with the drivers for now but I'll upgrade to 13.1 or whatever the current driver is at that time soon.

Thanks for letting me know underclocking works mrxenyo.

edit: It just crashed damn it.

Hmm. Well it sounds like your system is more stable at the lower clocks, just like ours, only in your case the effects are more pronounced. If I were you I'd try replacing the power supply with a heavy duty 700W from a reputable brand like Antec or Corsair as was suggested earlier. I intend to do the same myself. And if the price currently makes that impossible, maybe try swapping in a buddy's heavy duty power supply and see if that works?

I think the psu is going to be the next route I investigate simply because we've now ruled out so many other things (overheating, drivers, vbios versions, etc. etc.). 

Apple Cinema Display A1081 20" 1680 x 1050 (60 Hz)
Windows 7 Home Premium x64
ASUS M4A785TD-V EVO Mobo
AMD Phenom II X4 965 @ 3.4 GHZ (+ Hyper 212 Evo HSF)
AMD ATI Radeon HD 5870 1GB
8 GB DDR3 @ 1333 GSKILL
OCZ ModXStream Pro 600W modular psu

Here's an article on GPU power consumption that I found interesting. Worth reading!

EDIT: This is also a useful resource: http://www.extreme.outervision.com/psucalculatorlite.jsp

Apple Cinema Display A1081 20" 1680 x 1050 (60 Hz)
Windows 7 Home Premium x64
ASUS M4A785TD-V EVO Mobo
AMD Phenom II X4 965 @ 3.4 GHZ (+ Hyper 212 Evo HSF)
AMD ATI Radeon HD 5870 1GB
8 GB DDR3 @ 1333 GSKILL
OCZ ModXStream Pro 600W modular psu