How old is your computer? take a look inside, when its off, to check if the cpu cooler is full of dust, the cpu might be overheating. Are you sure you were using memtest86+, the old memtest will not check it properly.
edit: also what brand PSU are you using, whats its power rating, and what video card are you using. Your problem is most likely the PSU is faulty, but we don’t know that yet for sure.