I also think that it's either PSU or memory's fault. If it's some noname PSU that is most probably the culprit.

You can test memory with memtest86, although it's not memory's fault, it can also be motherboard's fault. I had similar experience few months ago. Computer rebooted itself at random times. Memtest showed errors, but with same memory on another computer memtest was fine. So I brought motherboard back to the store and they replaced it. New one works fine.