Have you run memtest86+
For you, it very well might be the psu, 350 isn't much but it can be enough. The key is quality and even the quality psu mfgs. let some bad ones through. If there are errors in memtest, it still can be the psu causing those errors. It may be a dual channel problem (I believe yours is 939) where the memory just doesn't like working together. The memory or core may need more voltage (both of which I don't like reccomending people play with eventhough its often a proven solution)
I don't mind going out to buy a psu to see if it makes a difference. I know I will eventually use it anyway. But for most if they go out and buy a $100 psu and it doesn't fix it they get really upset and have a delima of returning it or keeping it. Then, in the case of memory errors, go out and buy more ram... trying to find that seemingly mythical magical pair that actually works together.
It may also be a driver conflict. Even making sure bios, chipset and graphics drivers are the most recent may not be enough. Sometimes it gets picky on the order these are installed. Sometimes an older version of the driver actually works better.