I'd suspect a power issue, that is a 125W cpu afterall.. if your graphics card draws a lot of power too then that's more reason to think power might be the issue.
Cheaper power supplies will give an inconsistent supply of power to components.. that is, a cpu that you have working on 1.4 volts may want 1.42 volts to make up for inconsistency over reboots. Motherboards can be the cause of that too.
What I would try is finding the exact voltage specs for that cpu and setting it manually in the bios as a lot of motherboards (like my asus) overpower the cpu on default settings. My cpu uses at most 1.43 volts according the specs, yet the bios sets the power at 1.69 volts on automatic (causing extra power consumption and heat, not to mention it's risky).. actually I can use 1.25 volts at stock speeds and that works fine.
Another way to test might be to put a spare graphics card in that isn't very big or high performing as it draws more power, unplug your cd-rom temporarily, etc.. if all works fine after adjusting the voltages and doing that, then I'd suspect the CPU is the problem and just get a replacement from where you bought it from if that's a consumer right you have there or get it back on warranty as a last resort, otherwise upgrade your PSU .. the 'platinum' rated power supplies are the best you can get. Any branded 750 or 800 watt psu ought to cover all your needs however, and even a 650 or 700 may be fine. You can check how much power your graphics needs too to work it out, as CPU and graphics are the heaviest drawers of power. Other things like your cd-rom and hard disk will eat about 25-30watts total together.
Alternatively just set as many voltages in the bios manually as you can, just ram and CPU to play it safe (you can even try lower voltage like I did as the specs indicate a range usually), disabled unwanted features in there too. I'm not sure of how much your setup draws but a 600W seems a little low, other than that it could be motherboard issues as above, see if theres some firmware for your board and if the cpu compatibility is mentioned.