A few more random thoughts:
- 600 watt ps is not enough to run a 5870 and a 6870. Don't ask how I know.
Then you are doing it wrong
.
In all seriousness though, a good quality 600W power supply should be sufficient. What brand and model were you using, if I might ask? Seasonic PSUs are typically your highest quality power supply (and the companies they manufacture for, such as Corsair, except for their builder series). Lower quality power supplies, as well as using cheaper parts, can be unstable and often have a lot less than 600W available on the 12V rails (used for the GPU and CPU), not to mention being only barely able to handle their advertised load.