The PSU is horrible, yes, and I definitely think you should replace it, but I'm not sure that's the problem.
I'm guessing your RAM configuration is 4x2 and 2x2? Try taking out the 2 2GB sticks to see what happens. Weird RAM configurations like that tend to cause problems sometimes, and the sets are obviously not matched, so that's a concern, as well.
Also, if it's 4x3, that's a strange configuration as well, and it wouldn't surprise me to see that cause a problem either.
Either way, just try 2 4GB sticks.